It helps to think of the archivist as a divine wizard
That’s what he is, with a “prayerbook” instead of a “spellbook” but they work the same way.
Here, I’ll go through the two of them side-by-side to show you. Note that in all cases, when I say “wizard,” I am ignoring the Specialist option for wizards; the wizard in each example is a “generalist.”
Spells per day
A wizard may prepare a number of spells of each level as listed in their Spells per Day table, as well as additional spells for having a high Intelligence score.
An archivist works the same way, except the bonus spells are for having a high Wisdom score rather than Intelligence score. This change is important because everything else an archivist does is based on Intelligence; this split between Intelligence and Wisdom is known as dual-ability dependence, and is a pretty big deal (for example, a wizard could have a very low Wisdom score, relying on his strong Will save to counteract that, but an archivist needs Wisdom for the bonus spells).
Bonus spells are a mechanic common to all spellcasters; the only thing that changes is the ability score used. In all cases, these are only spell slots, not spells known. The amount of bonus spells is given in Table – Ability Modifiers and Bonus Spells.
Spells “known”
Neither archivist nor wizard knows spells the way a sorcerer does; they require an external aid, namely the prayerbook or spellbook. These books may contain many, many spells, but the archivist or wizard must prepare his spells per day (as determined above) ahead of time, so they only have access to a limited subset of the spells they “know” (that is, have in their prayerbook or spellbook).
Neither the archivist nor the wizard has a table indicating their spells known, because they may add as many spells as they can find/afford/fit into their prayerbooks/spellbooks. The table you see is for Spells per Day only.
Both archivist and wizard require that their Intelligence score (not bonus) be at least 10 + the spell’s level to add it to their prayerbook/spellbook, and they must be a high enough level to cast it in order to prepare it.
Other divine spellcasters, like cleric or druid, also must prepare their spells ahead of time, but need no book, since their spells come from their deity or divine forces. In a sense, the gods or powers that such spellcasters pray to form a gigantic “spellbook” for these classes.
Initial spell/prayerbook
A wizard starts play with a spellbook that has every cantrip from the Sor/Wiz list in it, as well as three 1st-level Sor/Wiz spells, plus an additional 1st-level Sor/Wiz spell per Intelligence bonus.
An archivist starts play with a prayerbook that has every orison from the Cleric list in it, as well as three 1st-level Cleric spells, plus an additional 1st-level Cleric spell per Intelligence bonus.
Free spells on level-up
A wizard gets to add two Sor/Wiz spells of up to the highest level he can cast to his spellbook every level.
An archivist gets to add two Cleric spells of up to the highest level he can cast to his prayerbook every level.
Additional spells
Here’s the tricky bit. Both archivists and wizards can add more spells to their prayerbook/spellbook. This costs money, but ultimately not that much money. They have to find the spells to copy them into their books, but this also means they can take advantage of a lot of spells they come across.
Wizards are fairly straight-forward. The spell must come from the Sor/Wiz list, and it must be copied from an arcane scroll or spellbook. For examples, a wizard could copy into his spellbook a scroll of protection from evil that was written by a sorcerer (i.e. arcane scroll, spell is on Sor/Wiz list), but not a scroll of protection from evil that was written by a cleric (on Sor/Wiz list, but not arcane), nor a scroll of cure light wounds written by a bard (arcane, but not on Sor/Wiz list).
Archivists are similar, with one major difference. Where a wizard must copy an arcane scroll or spellbook, an archivist must copy a divine scroll or prayerbook. However, where a wizard can only copy spells that are on the Sor/Wiz list, the archivist doesn’t care what spell list it is on. As long as the scroll or prayerbook is divine, the archivist may copy it, prepare it, and cast it (assuming they can cast spells of that level).
Balance and design
You seem to be a bit confused why things are the way they are, and you questioned the balance of things at least once, so I want to explain what’s going on.
To begin, the archivist is a phenomenally powerful class. It is one of the top five most powerful classes in the game, in fact. The wizard is as well, which is hopefully not surprising at this point since the two are nearly identical. The others are the artificer (Eberron Campaign Setting), cleric, and druid.
I’m going to ignore the oddball (the artificer); for the other four, all are considered to be in the top “tier” because they get extremely powerful spellcasting (up to 9th-level spells, the best there are, and from very good spell lists), and they can change which spells they have every day. That flexibility is fundamentally incredible, and it is that fact alone that separates these spellcasters from the next tier, which includes for example the sorcerer (literally the same list as the wizard, but can’t change spells so easily).
So yes, these classes are incredibly powerful. You’ll notice that three are from the original Player’s Handbook – Wizards simply underestimated what they could do, overestimated what other classes could do, and made mistakes making them.
The archivist was written much later, but was based on the cleric and wizard, so it inherited their power. Since the cleric could already access the entire Cleric spell list, the archivist needed something extra to justify the prayerbook: that extra something was the ability to scribe any divine spells, not just Cleric spells. The archivist also gets pretty nice class features, so it splits between Int/Wis instead of being pure Int or pure Wis. That’s how it got to be the way it is.
Best Answer
Specialization and Related Options
The extra spell slots are the intrinsic benefit of specializing, but they are not the only benefits: a number of wizard alternate class features only work for those specializing in a particular school.
Focused Specialization
Complete Mage gives an option to ban another spell school and give up a regular spell slot per spell level, for another two specialist spell slots per spell level. For most, this is a bad trade: banning three schools is a lot harder than banning two, and trading a regular spell slot for a specialist spell slot isn’t a great trade either.
Immediate Magic
Player’s Handbook II has options that allow a specialist to replace his familiar with a minor (...in some cases) magical effect that he may use as an immediate action, up to Int times per day.
Master Specialist
This prestige class from Complete Mage grants different benefits depending on which school of magic a wizard has specialized in. I’ll be considering it as a part of the potential benefits of specializing in a given school.
Specialist Wizard Variants
Unearthed Arcana has a number of specialist wizard variants, which allow him to trade away his bonus feats, his familiar, and/or his bonus specialist spell slots for bonuses that depend on his specialty.
Schools of Magic
Abjuration
Abjuration is certainly a potent school, not one that you want to be without. That said, a lot of the best abjurations are also on the cleric spell list—if you’ve got a cleric in the party, he may be able to handle abjurations, which could make it possible to ban abjuration safely. If you are a regular specialist (i.e. not a focused specialist, who needs to ban 3 schools), though, there are definitely better choices to ban. If you must ban 3 schools, abjuration is a viable choice, but only if someone else has abjurations. You do not want to leave your party without access to, e.g., dispel magic.
Specializing in abjuration is probably not the best choice, as far as spell slots are concerned. A lot of the best abjurations last a reasonably long time, and you probably don’t need a ton of abjuration-only spell slots. Still, it’s probably possible to find at least one abjuration of each level that’s worth casting at least once per day, so abjuration isn’t a bad choice by any means.
Focused Abjurer
Abjurations are good, but you don’t need abjuration spell slots this badly.
Urgent Shield
The abjurer’s immediate magic option is pretty mediocre: a +2 shield bonus to AC. You can get that with a mithral buckler (0% ASF, 0 ACP, so you take absolutely no penalty from it despite non-proficiency), which you can afford around level 5 or 6. It might be stylish for very-low levels, I guess.
Master Abjurer
The master abjurer is particularly good, making it harder to dispel your abjurations, combo evasion+mettle, and even, at higher levels, allowing you to center personal-emanation abjurations (read: antimagic field) on others (3/day, but still).
Unearthed Abjurer Variants
None of these is really worth it.
Resistance to EnergyResistance to one energy type, once per day, for one target, as a standard action. Not terribly impressive, and the amount of resistance is just 5 + ½ your wizard level. The familiar’s better, though this is probably better than urgent shield.
Aura of Protection+Int to AC and to saves, which is good, but only against the next attack/thing that requires a save, which is not. If this were the immediate magic option, it’d be worth considering, but it’s a standard action to turn on. Worse yet, it’s usable ¼ of your wizard level times per day, and replaces your bonus feats. Pass.
Spontaneous DispellingThis effect is pretty good; you can turn your lower-level spell slots into dispel magic or greater dispel magic, and don’t need to prepare it. It replaces your specialist slots, though, and burns yet more slots because you need four spell levels to manage dispel magic and seven to manage greater dispel magic. It’s decent, but ultimately I think the spell slots are better. It’s not like preparing dispel magic in abundance was ever a bad idea.
Incantatrix
Incantatrix (3.0 version in Magic of Faerûn, 3.5 version in Player’s Guide to Faerûn) is one of the most powerful prestige classes in the game (either version). Abusing metamagic is one of the most tried-and-true ways to break the game, and no one does that as well as an incantatrix. The 3.5 version requires you to have access (read: not have banned) abjuration. It was never a great choice for banning, but incantatrix means that doing so looks even worse.
Do note that incantatrix forces you to ban another spell school.
Conjuration
Conjuration is almost-certainly the most powerful school in the game. The only (mechanical) reason to ever ban conjuration is if you are intentionally nerfing yourself for the challenge or to avoid overshadowing others.
By the same token, conjuration is the best school to specialize in. Finding conjurations of each level that are worth casting is trivial—even non-conjurers probably prepare at least one conjuration of most spell levels anyway. From Core alone, grease (1st), glitterdust (2nd), black tentacles / dimension door / solid fog (4th), teleport (5th), greater teleport (7th), and gate (9th) are worth casting daily even if you didn’t have the specialist slots.
Focused Conjurer
As usual, not generally worth it, but conjuration makes a stronger case for this than any other school, because of its breadth. Conjurations can do almost anything, and that means you do not necessarily lose a lot of versatility by getting specialist-only slots.
Abrupt Jaunt
This is the ability to teleport a short distance 3+Int times per day, as an immediate action. That means 3+Int times per day, you can just say “no” to someone who attempts to attack you in melee. Make sure your DM understands the consequences of this before taking it; surprising the DM with this is liable to get you smacked with a DMG.
If you’re allowed, this is obvious. It’s absurdly good.
Master Conjurer
Extra hit points for your summons (not bad, but the death of a summon is rarely a tragedy), bonuses to your conjurations’ resistance to dispelling (quite nice, though with the right selection of conjurations dispelling is ineffective), and 3/day, a free Quicken Spell on a conjuration. Not the most glamorous of effects, but it’s decent. And of course, master specialist is a good prestige class anyway, and even if the master conjurer effects aren’t as good as some other master specialists, you’re still specializing in the best school.
Unearthed Variant Conjurer
All of them have to do with summoning, which is only one niche of many for a conjurer. Rapid summoning is basically must-have if you want to be summoning often, and enhanced summoning gives you a feat every summoner was probably going to take so why not. Spontaneous summoning isn’t worth it.
Rapid SummoningCast summoning spells that have a casting time of 1 round or less as a standard action. This is a must for summoners; the 1 round casting time of summon monster spells generally makes them a really bad idea. Works best in combination with malconvoker, and Cloudy Conjuration is a great choice for it.
Enhanced SummoningIf you’re a summoner (and not every conjurer is), you were probably going to take Augmented Summoning anyway. Scribe Scroll is nice enough, but I wouldn’t usually bother taking it if I didn’t get it free, which means I’ll take the feat I would have taken on my own instead.
The rest are not really worth as much as feats, to my mind, but they are good. You probably should never get them because you should be in some prestige class (except maybe the 5th-level one, but master specialist is better).
Spontaneous SummoningNot worth it at all. If you’re a summoner, you should just be preparing your summoning spells. If not, you don’t have any use for this.
Cloudy Conjuration
This feat from Complete Mage makes summoning spells produce a cloud of noxious gas around creatures you summon, and the summoned creature is immune to its effects. Everyone else in the area has to save vs. nausea, and cannot see clearly. When used with creatures that don’t need to see enemies to attack (say, fiendish monstrous spiders with their tremorsense), this is a really good feature. Does not actually require specialization in conjuration, but if you’re focusing on summoning spells, you should take rapid summoning (which does require it), and probably also the malconvoker prestige class (below).
Malconvoker
Doesn’t strictly require a specialization in conjuration, but to enter malconvoker (Complete Scoundrel) as a wizard and not be a conjurer is just silly. You should actually strongly consider being a focused conjurer—the class doesn’t make a lot of sense as an option if you aren’t filling almost every spell slot with some form of summon monster.
Usually summon monster is a little disappointing: they get a lot of creatures a whole spell level later than summon nature’s ally, with only the lackluster Celestial or Fiendish templates to show for it. With malconvoker, your summon monster spells get 5 spell levels’ worth of free metamagic applied to them (Extend Spell and Twin Spell). That goes a very long way to making up the difference. Also, just personal opinion, but I think the flavor is really cool.
Divination
Divination cannot be banned, period, so that’s not a hard question to answer.
Specialization in divination is interesting, however: you only have to ban one school. Ultimately, in Core, this is probably not really worth it: there are only so many divinations you need to cast in a day. Divinations are powerful, but there isn’t really a Core divination at every spell level that I could see using every single day.
With supplements, particularly Spell Compendium, making good use of those spell slots gets a lot easier.
Focused Diviner
Remember how it was hard to fill those specialist slots? Now you have three times as many to fill. Banning a second school can be easy for a focused diviner, but those one spell slot for anything is better than two divination-only spell slots.
Glimpse Peril
This immediate magic gives you a +2 bonus on your next saving throw. Good, in that you can use it right before you need to make one. Bad, because it’s kinda small, it’s 3+Int times per day, and familiars are pretty good. Overall, I’d say it’s a toss-up: you could do much more with your familiar, but if you don’t really care about it and won’t bother, might as well get something you’ll actually use. But then enhanced awareness is probably better.
Master Diviner
First, spells you have to concentrate on remain going after you stop concentrating, which is great. Then you get uncanny dodge, which is not bad by any means. Then you get to add true seeing, for free, on top of any other divination spell you cast, 3/day. That’s great. Master diviner is definitely one of the better master specialists.
Unearthed Diviner
All three of these have their uses.
Enhanced AwarenessEnhanced awareness is pretty solid. So are familiars, if you know what you’re doing, but these are much more straightforward and easy-to-use bonuses. I’d take it.
Bonus Feat ListImproved Initiative is the only good feat here, but if you need one of these feats for a prerequisite, or like Improved Initiative over a metamagic feat, go for it.
Prescience+Int on your choice of a whole bunch of things? Not bad. Free action, out of turn if necessary? whistle The daily limits on this are very tight, though. The cost is high too.... except that diviner specialist slots are less valuable than other schools’. Tough call, which is a sign of good balance. Could go either way.
Unseen Seer
Another prestige class that doesn’t require you specialize, but the unseen seer’s all about divination, in a really cool way: it's the magical espionage class. Great skills, advancement of sneak attack or similar (but you need to have that from somewhere else), bonus divination spells from off your list; this is a great prestige class.
Enchantment
Enchantment is a school that I really like. My first character was an enchantment-focused con artist sorcerer. In a low-level, urban campaign (i.e. around a lot of humanoids), it can be phenomenal.
That said, enchantment is the first school to ban. It’s got a lot running against it. One, every single spell in the school is [Mind-Affecting]. Constructs, oozes, plants, undead, and vermin are all immune to those by default. Mind blank, at high levels, makes pretty much everyone else immune to it, too. Protection from evil et al. block all compulsions that control someone, which is an enormous chunk of the school.
Worse yet, nearly every single enchantment is a save-or-lose—something that wizards have from basically any other school. Sure, in the case of dominate, it’s save-or-a-fate-worse-than-death, but with that being the case, people are going to find protection from it.
Specializing in enchantment is... problematic for the same reasons. The school is not versatile. All those enchantment-only slots are going to be doing a lot of the same things. And you’ve lost the easiest-to-lose school as an option, which means you will be losing something you really don’t want to, like abjuration or necromancy.
Focused Enchanter
Don’t even consider it. At that point, play a beguiler.
Instant Daze
If it weren’t for the “compulsion, mind-affecting” bit, this would be worth it without a doubt. As is... if you’re in a campaign where enchantment works (i.e. not fighting a lot of things with immunity to it), this can be quite useful.
Master Enchanter
The minor enchantment esoterica is excellent. Every enchanter should get that. The moderate and major are both “save twice, take your preferred result” abilities, which are awesome. Enchanter is not a great choice, but master enchanter is a great class for one.
Unearthed Enchanter
CohortA meh version of Leadership. Leadership is broken, so this is powerful, but just take Leadership if you’re doing this. Or do it right, and go for thrallherd.
Social ProficiencyGreat skills, so this is cool. The +2 bonuses are insultingly bad, not even close to being worth feats, but you should be going master enchanter anyway so that won’t matter.
Extended EnchantmentFree Extend Spell on enchantments, 1+½ Enchanter level? That’s not bad. Losing those slots hurts, but... a lot of them were going to be kind of redundant anyway, enchantment being as one-dimensional as it is.
Mindbender
This prestige class from Complete Arcane is bad. It focuses on enchantment, loses a bunch of spellcasting levels, and just, is bad. However, Mindbender 1 is excellent: it gives you telepathy out to 100 ft. You can enter at level 6, and immediately take the Mindsight feat from Lords of Madness. This is excellent.
But you don’t have to be an enchanter to get in, which of course means that you are better off not being one.
Anima Mage
This prestige class from Tome of Magic is the “theurge” class for arcane spellcasting and the binder class. Binders are awesome, and with Improved Binding, you can get into anima mage with only one Binder level, which is way better than most theurges. Plus it has actual class features, pretty good ones at that. Pretty solid class. Doesn’t usually have much to do with enchanters specifically; any wizard specialization can qualify (which means others are better).
However, it’s worth noting that under stupidly-strict readings of the rules, an enchanter can start the class at 2nd level, with no binder levels, and end the class with the spellcasting of an 11th-level wizard and the binding of a 10th-level binder. You should never do this, it’s stupid, but for more details, see here
Evoker
This is the second school to ban. A lot of people might gripe about this, but it’s true.
Blasting is a fairly sub-optimal strategy. Damage whittles enemies down, and in the meantime they are 100% effective. Other schools can make one failed save game-over for the target. Sometimes, they don’t even have to save.
Other schools have blasting. Conjuration, in particular, has a bunch of SR: No nukes. Like orb of force, which is extremely reliable damage: SR is a bigger problem than a touch attack, which makes orb of force often more reliable than magic missile. Evocation really shines with area-affecting blasts, but these are usually suboptimal because you’re spreading damage around (and risking friendly fire), rather than focusing something down and killing it.
Damage steps on other characters’ toes. There are unfortunately quite a few classes for whom damage is the only thing they can do. Wizards have other options, you don’t need to hog the damage spotlight.
Shadow evocation can get you a lot of the best evocation effects despite banning it.
Those three reasons are also why you shouldn’t specialize in evocation. For pure-damage blasting, conjurer is probably better. Actually, sorcerer is probably better. Sorcerers get a few sorcerer-only spells that are excellent for a blaster.
Focused Evoker
Just, no.
Counterfire
Minor damage that revolves around you taking a hit. Stick with the familiar.
Master Evoker
A bonus on Concentration checks that you shouldn’t need, decent resistance, and a half-Repeat Spell 3/day. Yawn. One of the weaker master specialist options, on top of an already-weak specialty.
Unearthed Evoker Variants
Energy affinity and substitution aren’t bad, but overcome resistance is a waste of time.
Energy AffinityA +1 to caster level is a good thing; that’s probably worth a familiar if you build around it. Too bad force isn’t an option, though. You’ll be investing in Searing Spell or Piercing Cold, most likely.
Energy SubstitutionBetter than the feat, so if you were going to take it, might as well get it this way. Not like you’re missing all that much from master evoker anyway. Make sure your DM okays this qualifying as the feat for prerequisites if that’s relevant to you; technically it never says it counts as the feat so, RAW, you wouldn’t.
Overcome ResistanceExtremely limited uses and cannot break immunities. Even evocation-only spell slots are worth more than this.
Contingency
Contingency is the best evocation in the game.
Contingency very well may be the best spell in the game. Contingency alone is a reason not to ban evocation... or it would be if it weren’t for greater shadow evocation. Or Craft Contingent Spell, which is just super-broken.
The reason contingency is so good is because it throws the action economy out the window. Contingency happens instantly, and if you word things wisely, exactly when you need it to.
One of the best suggestions for a 3.5 Wizard Duel that I’ve ever heard was that the two wizards sit down at a table, each drinking the beverage of his choice, and go over each others’ lists of contingencies (from Craft Contingent Spell). Because both are so Intelligent, both can see who would come out on top, and both can see it’s better if they simply agree on this and don’t actually waste their resources on the fight.
Resilient Sphere
This is kind of a pattern: evocation is almost-all blasting, which is bad, but its few non-blasting options are its best spells. Resilient sphere is a save-or-lose that targets Reflex—often a low priority since it’s usually only defending against blasts.
Force Missile Mage
A prestige class from Dragon vol. 328 specializing in magic missile. Kind of fun, and magic missile is one of the better evocations. Not really a good class but it’s cool and evocation-related.
Illusion
Illusion is a great school, the source of a lot of the wizard’s defenses. A specialization in illusion is totally respectable, the school has a lot to offer. Banning it is unwise; you’ll miss the many defenses, and losing shadow evocation means you either need to not ban evocation, or give up contingency. Neither is ideal.
Focused Illusion
Probably not, but illusion’s a better school for it than many. The killer gnome certainly would.
Brief Figment
I don’t see how this is supposed to work. As an immediate action, which means it should be really obvious which of you is the real one. Don’t see a lot of point. If it works like mirror image, though, that would be pretty worthwhile. But notice that abrupt jaunt is literally strictly superior: this is a 50% chance to not get hit by the first attack. Abrupt jaunt is a nearly-100% chance to not get hit by the whole full-attack sequence.
Master Illusionist
Nice buff to save DCs, free concealment, and 3/day your spells are basically purely-mental actions. That’s a plenty-solid list right there. Definitely a nice option.
Unearthed Illusionist Variants
Chains of disbelief is great, shadow shaper’s OK, illusion mastery is bad.
Chains of DisbeliefYou want this. That save bonus from someone pointing out your illusion is rather large and the odds of someone making the save when you’re trying to fool a whole bunch of people is large.
Shadow ShaperThese are pretty cool; you have to be an illusionist 20 to get them all, which is a pain, but if you’re going to do that, I’d definitely consider these.
Illusion MasteryAdding spells to your spellbook is cheap; spell slots are worth way more. Even if you want this effect, the Collegiate Wizard feat (Complete Arcane) gets it without giving up spell slots.
Shadowcraft Mage
This prestige class from Races of Stone is absurd. Built right (look up the killer gnome), it can use silent image as a cantrip that mimics any spell in the game, with greater-than-real reality so that people who make their disbelief save take more damage (if you go by RAW). This class can also quite potent without cheesing it out. Doesn’t require specialization but since your illusion spells can do anything, no reason not to have more of them.
Necromancy
Necromancy, for a wizard, is not really about having a horde of minions. Go for cleric or dread necromancer if you want that. Animate dead means you can have a fair few minions, but ultimately other classes are better at it (rebuke undead, desecrate, etc.) and going down that route misses the point of the Sor/Wiz necromancy spells.
Sor/Wiz necromancy spells are about curses and other potent debuffs, and oddly enough, also quite a few buffs. Lots of necromancy debuffs are rays, which means they are often no-save, just a ranged touch attack. Touch attacks are easy, so this is a great thing. Enervation is the quintessential Sor/Wiz necromancy spell. Ray of enfeeblement is another great one. On the buff side, you have false life and the like, which are quite good.
So specializing in necromancy is workable; there’s some great spells and some solid breadth. On the other hand, you can ban necromancy: other schools have buffs and debuffs. Maybe not quite as good as some of the best in necromancy, but banning a school shouldn’t be painless.
Focused Specialist
Probably not a great idea. Necromancy has some decent breadth, but not that much (like conjuration or illusion), so you’re going to want other schools’ effects.
Cursed Glance
Much better than counterfire, but ultimately not that great. The debuff is nice enough, but you really don’t want people targeting you.
Master Necromancer
Lots of undead-ally buffing, which is kind of missing the point for a wizard necromancer, but the effects are good and you should have at least a few. The moderate effect is excellent, giving you immunity to a lot of things you really want immunity to. Not trivial stuff to get immunity too, either.
Unearthed Necromancer Variant
None are really great, but skeletal minion’s close to worth it.
Skeletal MinionBetter combatant than a familiar, but ultimately the familiar has a lot more options available to it. Better (and more thematic) than a stock-standard familiar, but if you put some work into the familiar, it can be a lot better than this. Up to you if you care enough to worry about the familiar.
Undead AptheosisThese are all pretty meh. You want immunity to these things, not minor boosts to your defenses against them. Immunity would be way too good, of course, but still. Ultimately, Necromancer 20 isn’t what you want, so this doesn’t really matter.
Enhanced UndeadNot really worth it, though the effect is good. Again, if you want a horde of undead minions, you want cleric or dread necromancer.
Incantatrix
As discussed earlier, this is a ridiculously-powerful prestige class. It requires that you have abjuration, but otherwise is agnostic towards spell schools. Why bring it up here?
Because necromancy makes a great choice for a third school to ban on an incantatrix, because spells you already know when you enter incantatrix remain usable. A lot of the best necromancy spells are low-level, and benefit immensely from metamagic, which is incantatrix’s schtick. Get enervation before going into incantatrix, and you’ll never miss those higher-level necromancy spells. A heavily-metamagic’d enervation is vastly superior to energy drain.
Transmutation
The other “big” school; in Core, transmutation actually has more spells than conjuration. This school is fantastic.
Transmutation has great buffs and great debuffs, including crowd and battlefield control. It’s got a few blasting spells.
And polymorphing is one of the tried-and-true ways to break the game. Even wizards admitted that their monster designers really didn’t consider what would happen when players got access to a monster’s abilities. It starts at level 2, with alter self—if you get a nasty type, like Aberration, Dragon, or Outsider, you can alter self into some really dangerous stuff. From there, it just gets a lot, lot worse.
Even without ever using a polymorph spell, though, the school is good. Transmuter is totally viable. Banning Transmutation is silly, and almost no one ever does it, for the same reasons they don’t ban Conjuration—it’s just too good.
Focused Transmuter
Like conjuration, transmutation has the power and the breadth to be worthwhile for focus, but really unless you’re abusing polymorph it’s probably better to get those normal spell slots. A smart wizard shouldn’t be hurting too badly for spell slots.
Sudden Shift
Kinda pointless as an immediate action, since it only lasts 1 round. Still, flight at level 1. The familiar is probably better, though.
Master Transmuter
The first one is pretty awesome. The second one’s OK. The third is bizarrely weak. Kind of the opposite order you’d expect them in. Still, master specialist is good and the minor school esoterica, in particular, is great.
Unearthed Transmuter Variants
Enhance AttributeNot good enough to replace the magic items, which means you won’t bother using this after level 6 or so. Since when does a wizard care about anything but Intelligence anyway? (slight exaggeration) Especially a transmuter, who may very well be spending a lot of time in an alternate form that replaces a lot of his ability scores.
Spell VersatilityThis is pretty awesome, though I strongly recommend trying to avoid hitting Wizard 5 (for example, by taking levels in master transmuter) until just the right moment so you can get a particularly great spell. Like.... contingency. Yeah, definitely contingency.
Transmutable MemoryThis is probably one of the best of these abilities, since it doesn’t have a built-in inefficiency the way many of them do. Still, transmutation spell slots are valuable... which makes this pretty well balanced, one way or the other. Do remember, though, that you can leave spell slots unprepared, and prepare them in the middle of the day in fifteen minutes. This takes less time and lets you rearrange spell slots in interesting ways, so it is better, but be aware.
Master Transmogrifist
It gives up spellcasting levels, to improve one of the most broken lines of spells in the game. Only worthwhile if you’re abusing polymorph. It’s better for everyone that you just don’t.
Conclusion
Enchantment and evocation are your first two choices for banning, and neither is a good choice for specialization. Any of the remaining schools are viable specialties, but conjuration and transmutation are the best because they’re the biggest and most powerful. If you must ban a third school, abjuration’s a good choice if you have a cleric teammate who can use those spells instead, otherwise necromancy is probably the least-painful.