Paladin 2 / Wizard (abjurer) X
You said you are willing to take at most a 2 level dip in another class for proficiencies. Have you considered taking these levels in Paladin? Assuming you want to keep the "I'm a Wizard!" flavour, taking your first 2 levels as a Paladin of the god of magic (assuming there is one in your campaign, of course) isn't really out of character. So here's my take on this build. I'll mostly cover melee options, since this is what the question is about, but you should still be able to do anything that another wizard could do, just 2 levels later. This gap can be great at certain levels (Fireball is a great damage upgrade at level 5), but it shouldn't be noticed too much on single target damage (Smite!). It's not the strongest build out there, but it's definitely good enough to be enjoyable!
Benefits of 2 paladin levels :
- Proficiency with all weapons : opens up many solid weapon choices
- Proficiency with all armors and shields : although dex is definitely the best stat in 5E, a melee wizard will require spending spell slots on defence to keep up. Being able to wear a full plate and a shield gives great defensive benefits and costs no daily ressources.
- 6 more HPs : While 2 more level wizard levels would've given you 4 more arcane ward HPs, those only replenish on a long rest or by spending spell slots. Arcane ward is an awesome feature, but real HPs trump it anytime.
- Lay on Hands : Yay for 10 free HPs per day! More than makes up for those 4 lost ward HPs, and can be used on other people, too.
- Fighting style : There are many good options here, but I'd go for protection or defence to increase your utility/survival. Great weapon fighting is a good offensive option if you forgo your shield and grab a great sword, especially since you're going to stack lots of dice on those attacks. This can be somewhat replaced by the Elemental Adept feat, however.
- Access to 1st level paladin spells : One thing you'll have as a wizard is lots of low-level spell slots rather early. Smite spells might not always be the best options, but they can add good damage and other effects on your melee attacks. Paladin also has a few abjuration spells, which gives you back some arcane ward HPs, but the good ones are higher level, sadly. If you have the warcaster feat and can handle your constitution saves, Shield of Faith is also very good as a low-cost defensive boost. While Cure Wounds is a paladin spell, you can cast it using your full spell slots, which means that, although not a cleric, you still have access to some great healing powers if they are needed.
- Divine Smite : Convert spell slots into damage. Given that you can elect to smite after you know the attack hits, and that there is no save for this damage, it's a great way to increase your melee damage. Especially good if you crit...
That being said, given equal gear, you should have the same AC as any other tank, since you're wearing the same stuff they are. As for your damage, the new Sword Coast Adventure Guide cantrips are there for you. Sure, they're not going to out-damage a fighter or a rogue, but they're still very good damage options. Since they require a melee weapon attack, they also trigger class features such as Divine Smite, so you don't miss out too much. Having two attacks could technically mean 2 smites per round, but the added damage of your cantrips will compensate for this quite decently.
- Green-Flame Blade : when fighting multiple enemies, this attack basically gives you the benefit of a second attack without costing anything. Since you're not going to have multiple attacks from class features, this is pretty much as good as you're going to get.
- Booming Blade : Assuming you can make sure your opponent moves willingly each round, this cantrip will give you the same benefits as GFB except on a single target.
Other thing to note is that the secondary damage from these spells automatically hits, no save and no attack roll required, which means that you can strike a minion to land free damage on the BBEG. These spells will thus give you decent damage round after round, leaving you with all your other spell slots to use as you see fit. Your 2 levels of paladin will give you the opportunity to convert your low-level spell slots into more damage as an option, and your wizard powers will allow you to turn these same spell slots into defensive abilities. Shield will grant you +5 AC for one round, which is awesome if you attract the BBEG's attention (especially given that your AC is already high). In Elemental Evil, there is also the Absorb Element spell, which gives you resistance against a single element, also for one round. This gives you defensive options for both physical and most magical attacks. As an interesting addition, both of these spells are abjuration-based, and will thus heal your ward for 2 HPs every time you cast them.
And after all this, you're still an almost full wizard. Your access to spells and features will be delayed for two levels because of multi-classing, which shouldn't reduce your melee effectiveness, but you will still have access to 9th level spells and have spell slots as a 19th level caster. While the Signature Spell capstone is good, the real treat is at wizard level 18 (character level 20 for you), so you don't miss out on much. Indeed, spell mastery will allow you to have 2 low-level at-will spells, which gives you infinite Shield spells, for instance. This should allow you to use your slots for more offensive options, since your defence is free. Infinite Shield spells also means that your arcane ward is always topped off after every combat if you take a minute or so to recharge it after each fight.
Your melee power also scale quite decently if we compare them to a tank fighter (longsword + shield, defensive fighting style) of equivalent level :
- Level 1-4 : Fighter [1d8 + str] vs GFB [1d8 + str + (int secondary)]
- Level 5-10 : Fighter 2x[1d8 + str] vs GFB [1d8 + 1d8 + str + (1d8 + int secondary)]
- Level 11-16 : Fighter 3x[1d8 + str] vs GFB [1d8 + 2d8 + str + (2d8 + int secondary)]
- Level 17-19 : Fighter 3x[1d8 + str] vs GFB [1d8 + 3d8 + str + (3d8 + int secondary)]
- Level 20 : Fighter 4x[1d8 + str] vs GFB [1d8 + 3d8 + str + (3d8 + int secondary)]
Of course, a fighter has abilities to increase his damage, but so do you (thank you, Divine Smite)! Since the fighter has more attacks, he's more likely to deal some damage each round, whereas your damage all hinges on your single attack landing. This will be especially important if the fighter can get his hands on a weapon that deals extra damage (like a flame tongue), an ability that would be mostly wasted on your single attack per round. The fighter also only requires only one good stat to be 100% effective, while you will need both strength and intelligence. Since your intention is to go melee, I'd consider maxing strength first, especially considered you'll use your spells mostly defensively or in a utilitarian fashion (so lower save DCs are not as bad).
Feats to consider :
- Warcaster : For pretty obvious reasons (casting and adv. on constitution saves). Combined with Booming blade, it's also a boost to damage: when an enemy tries to get away, you booming blade it, which will deal almost double damage if it hits, as the enemy will likely leave the area right after. If they don't, well, your party gets to kill them anyways.
- Shield Master : If you are using a shield, it's a solid defensive feat.
- Heavy Armor Master : +1 strength, reduce most physical oncoming damage by 3. The drawback is that it doesn't work on your arcane ward, as it has it's own HP pool. As such, any damage the ward takes is not "damage that you take" and does not trigger this feat. Still a great option for a tank, especially one that has a wizard's HP pool and requires strength for his attacks.
- Elemental Adept : You're going to cast a lot of fire cantrips, and this feat allows you to ignore resistance and to treat 1s as 2s. This feat does not specify that only the fire damage dice are affected, so it works on your weapon die, your GFB dice, but also on your added Divine Smite dice. Definitely not bad.
- Mage Slayer : Disrupt enemy spellcasters from melee range. The attack granted by this feat is not as strong as a full opportunity attack (as warcaster will allow for a GFB or BB cantrip), but if you can prevent them from casting, it has a lot more utility. Advantage on saves isn't exactly bad either.
Other things to consider :
- Transmuter instead of abjurer : possible proficiency with constitution saves or resistance to one element is a good trade-off for a melee wizard. Not sure that I'd sacrifice arcane ward for it, though. Since Arcane Ward has it's own HP pool, all the damage it soaks isn't counted towards the concentration save DC. Advantage from warcaster should be more than enough, especially if you have some stat bonuses.
- Bladesinger instead of abjurer : A tough one... Since you're going to use cantrips for offense, you're wasting the extra attack feature with that build. But... a dex-based character wearing light armor will have only 1 less AC than a plate wearing character (equal if you cast mage armor instead), so your bladesong will leave you with a net +2 to AC during a fight once you get 20 intelligence (since you're also forgoing your shield). Even if not going for a strength build, you lose none of the advantages of a paladin (smite, armor proficiencies, healing, spells, etc.), but also gain Intelligence bonus to concentration saves and increased combat speed, as well as overall better skills since dexterity is the best stat. I'd personally favour bladesinger, but both options are very interesting.
Tl;dr: Bringing Intelligence up to 20 is necessary at some point, but doesn't have to be immediately. War Caster and Resilient are both great options and will help you maintain concentration. Heavy Armour Master and Lucky are also great options but won't have much impact on concentration. None of the other feats seem particularly worthwhile for you. Personally, I'd probably take War Caster and then decide between Heavy Armour Master and bringing my Int up to 20.
I'll address your points one by one, starting with:
Bringing Intelligence up to 20
You definitely want to bring your Int to max at some point, because it controls your primary means of attack. The question is whether you want to get it now, or leave it till later. With that in mind, consider what 2 more points of Int actually provide:
- +1 to hit with your spell attack
- +1 to DCs for your spell saves
- +1 to Int saves
- +1 to Int checks
- +1 to number of spells you can prepare
None of these are huge benefits in the short-term. Long-term, this makes you 5% more effective at most of the things you specialise in. (Warning: gross over-generalisation.)
War Caster
You don't intend to have both hands full, so this only gives you advantage on Con saving throws to maintain concentration, and spells for opportunity attacks. However, both of these are strong benefits. Advantage to maintain concentration needs no explanation, but spell opportunity attacks might not be as clear.
To start with, you're planning to be in the thick of the melee, so you should be getting opportunity attacks often enough to want to use them. Unfortunately, you aren't planning on using a weapon, and your signature spell Vampiric Touch won't work with opportunity attacks. (It specifically requires an action on your turn to make an attack with it.) So in your present state, you have no use for opportunity attacks. Giving yourself an option could pay off.
On the other hand, opportunity attacks aren't the only reaction, and you might want to save your reaction for spells like Shield or Counterspell. That said, these require resources, whereas with War Caster you can always use your opportunity attack to cast a cantrip.
Heavy Armour Master
As you say, the Strength is negligible where you're concerned, so the question is the damage reduction. This is a great option for someone planning to be in melee - 3 damage off every non-magical weapon attack adds up to be a lot of damage very quickly.
For concentration, it's a bit weird. It won't affect the vast majority of Con saving throws you make to maintain concentration, since the damage has to be at least 22 for it to have an impact. (Many high-damage attacks are magical, and it won't affect those either.) When it does affect the DC, it will only reduce it by 1-2. So as an option to help you maintain concentration it's a bit of a bust. It's still a great defensive option though.
Keen Mind
I can't say any of these features have ever come up in a game I've played. They're all highly situational and I can't find anything to redeem this feat other than "it's kind of cool, I guess".
Linguist
3 languages is pretty good, but there are spells that take care of this sort of thing for you. I've never seen a situation in game where a cipher would've been handy. If you're looking for a way to send messages to someone that no one can intercept, there are a variety of spells to achieve that.
Lucky
3 rerolls a day that you can choose to spend once you've seen the result? This is huge. You can spend them on an attacker's roll against you? That is just nuts. If you get critted, you can just wipe it away. Note that its benefits aren't nearly as potent on rolls that you make with advantage, but they're even more helpful on rolls you make with disadvantage. As far as concentration is concerned, you can fix a failed concentration roll 3 times a day, but you're likely to be making a lot of them, so something that isn't a scare resource and benefits all of them is probably worth getting.
Observant
This feat is frighteningly good. Just not for you. For a character who's maxing Wisdom and has proficiency in Perception, this makes them a portable radar station. (One of my players, the cleric, took Observant and has been making my life hell spotting every stealthed enemy and trap a mile away.) For you, it will make you almost as good as they were without it. If your party lacks a "sensor" character, it could be worth considering. Assuming you have one, I don't recommend this.
Everything in the above paragraph is based on Perception, without considering Investigation. That's because Perception is used far more often than Investigation, and passive Perception is used almost constantly whereas passive Investigation rarely sees the light of day. This can vary from campaign to campaign, obviously, but in general Perception is better.
Lip-reading is a cool little feature that I have seen used several times in intrigue situations, but I don't think it's worth spending a feat on.
Resilient
For maintaining concentration, this is pretty strong. More reliable than the advantage provided by War Caster, and scales better as you level. As well as that, though, there are a lot of effects that trigger Con saving throws. Most diseases, poisons, many spells, and a lot of monster effects. There's a saving throw for every stat, but Con, Dex, and Wis are still the most common, so this is definitely worth your consideration.
Ritual Caster
First and foremost, you have every benefit of Ritual Caster (as far as spells on the Wizard list are concerned.) Second, the benefits of this particular feat are highly dependent on what scrolls the DM feels like tossing your way. So the only quantifiable benefit of this spell for you is learning 2 1st-level spells from another class's spell list. Unless you can see something you really want (I can't), I can't recommend this.
Besides that, most rituals are either available to the Wizard or can be effectively duplicated by the Wizard. The only one I can see that you can't produce for yourself (barring a Wish, obviously), is Silence, which I can't quite see how you would use as a ritual. (It's more of a combat spell, and the 10-minute casting time is inconvenient in combat.)
Best Answer
There are a few reasons for a spellcaster to be in melee (most of which you mentioned.) I'll cover them one by one.
One is auras that buff nearby allies. The Paladin wins this one. Honestly, no other class even comes close. However, outside that, the Paladin's primary focus is on buffing his own melee attacks with the [X]-ing Smite spells, which isn't exactly what you're after. Also, as a half-caster, the Paladin is almost certainly not what you're after.
The next is spells that damage nearby enemies. The standout here is the Cleric's Spirit Guardians, which, once cast, damages everything around you for up to 10 minutes without requiring any further actions on your part. Other notable spells include the Paladin's Destructive Wave and the Warlock's Arms of Hadar. There's not too many spells in this category, unfortunately. The Elemental Player's Companion addded some good new ones to look for - Thunderclap is a cantrip that's just perfect for a melee spellcaster, and Earth Tremor is a pretty awesome too.
Reason number three is if you want to be attacked for some reason. The Wizard's Fire Shield is probably the best spell for this, but the Warlock's (or Tiefling's) Hellish Rebuke or the Tempest Cleric's Wrath of the Storm ability work here too.
Next up, spells that have their origin on you. Burning Hands, Cone of Cold, Thunderwave, etc. There's a lot of these, but none of them really stand out, no class is particularly better at them, and most of them don't really require you to be in melee anyway. They're good, and you'll want to have some of them, there's just not much to say about them here.
Finally, melee range attack spells. (And yes, I saved the best till last.) There is a definite winner here: Vampiric Touch. A minute of powerful melee spell attacks that do a fair bit of damage and heal you? Perfect. It's available to a few classes, but the one that gets the most out of it is a Necromancy Wizard, because Grim Harvest will get you even more healing when you kill something with Vampiric Touch. If your DM will allow it, the Death Cleric from the DMG also gets pretty good with this spell, with Touch of Death, Inescapable Destruction, and eventually, Improved Reaper (!!!).
I'd probably recommend the Necromancy Wizard or the Death Cleric, but whatever you choose, you are going to run into one problem: concentration. Most of the good spells I've mentioned require concentration, which means you can only use 1 at a time, and you are liable to lose the spell when you get hit by attacks. Which, as a melee spellcaster, is probably going to be often. Concentration checks aren't particularly difficult, but if you have to make a lot of them you might consider investing in a method of gaining advantage or proficiency on them. The War Caster feat gives advantage, while the Resilient feat, Sorcerer, or Barbarian give proficiency. Of course, there are a lot of ways to give advantage on or boost any roll, so you might not find this a problem.
On Wizard schools specifically:
Abjuration has some great benefits, but the only one that is particularly good for a melee is the Arcane Ward, which effectively soaks one hit per day, plus a little bit more every time you cast an Abjuration spell. Not bad, but not great.
Conjuration has Focused Conjuration, which allows you to ignore damage for concentrating (great!) but only for Conjuration spells, of which there aren't many that suit you.
Divination has nothing that works specifically for your purposes.
Enchantment actually has one ability that's great for this: Hypnotic Gaze. It effectively allows you to lock down a single creature in melee.
Evocation is great for evocations (as you might expect), and most of the damage spells with you as the origin are evocation, so definitely worth a thought.
Illusion has an auto-miss reaction, which is cool, but not much else.
Necromancy has the aforementioned Grim Harvest, which is pretty good, and Inured to Undeath, also pretty good (but only when fighting undead), but its other features are more geared around having an army of undead fighting for you, which is pretty powerful, but not really what you're after.
Transmutation doesn't have all that much for a melee, except that you can get a free proficiency in Constitution saving throws, which will help you maintain concentration.
On Shield Master specifically: for you, it's almost completely junk. It boosts your Dexterity saving throws, and nothing else. I'd really recommend against taking it. Heavily Armoured, on the other hand, will take your AC from a maximum of 17 (assuming you have a Dex modifier of +2), to 18, with no investment in Dex required. With the houserule in place that gives you shield proficiency as well, it pushes your AC up to 20 - at this point it goes from good to downright amazing. AC is quite rare and valuable in 5e, especially if you're used to 3.5 and everyone walking around with AC 30.