First of all, the Prestige Class Tier List is not nearly as widely-ascribed-to as JaronK’s base class one. For one thing, it is much harder to judge a prestige class (especially ones that can vary so much depending on how you enter), and for another there are just so many more of them.
Take the Shadowsun Ninja. For a Monk, it’s a dramatic step up; for a Swordsage, it’s... a thing. There are some neat tricks possible with it (Tomb-Tainted Soul or the Undead type allow you to use the negative energy for healing while using the positive energy on your allies, so that’s indefinite healing), but ultimately it doesn’t really change much about the Swordsage’s tier.
The problem of the Master of Nine is that it requires a ton of feats. If you aren’t a Swordsage, it also requires multiclassing, but that’s not really a bad thing for initiators. In fact, judicious multiclassing helps a great deal with the feats, because one level in Cleric gets you two of the feats (Darkness or Shadow domain gets Blind-fight, Time domain gets you Improved Initiative). The unarmed Swordsage adaptation also gets you Improved Unarmed Strike, and most Swordsages want Adaptive Style anyway.
That leaves only Dodge to be picked up. Several options, including Tome of Battle’s own Desert Wind Dodge, are better than ordinary Dodge, though even the best is still weak. Still, one feat burned and the single-best-dip-in-the-game (don’t forget that Cleric 1 also gives a few spells, and Turn Undead can be used to fuel the often-excellent [Divine] and [Domain] feats) is not too high a price to pay for the excellent class features that Master of Nine offers.
The limited Dual Stance feature is not nearly as good as the Warblade’s version of the same, but it’s still awesome and you can get it way sooner than 20th level. The eight maneuvers in five levels, of course, is phenomenal, and a maneuver readied per level is insane.
If you try to get into Master of Nine as a regular, single-classed Swordsage, you’re making a huge mistake and will regret burning all of your feats that way. If you’re clever about picking up feats, though... the class can be excellent.
Side-note: you don’t lose “more” by taking another level in addition to Cleric 1 with your Swordsage levels, because other class levels count half for your initiator level. There are a lot of great options for that extra level. Fighter or Psychic Warrior could be used to get another feat, to make up for the one lost picking up (Desert Wind) Dodge. Psychic Warrior also grants you a single power – which could be expansion, for instance, a great choice. Barbarian gives a ton of stuff on level 1 as well (don’t forget to check the various alternatives for Rage for the one that best works for you).
The easiest way to emphasize your casters in the early game, is to throw in lots of relevant skill checks, particularly knowledge or spellcraft checks. Almost any spellcaster is going to have relevant skill modifiers, and it proves their place in the party.
A related option is challenges tailored to make spells useful. A small item you need is on the far side of a chasm? Summon Nature's Ally or Mage Hand can help with that. Having ambient magic, or an arcane trail to be tracked with Detect Magic also calls out your casters.
Also, it's been my experience that Druid is one of the better low level caster classes, with cleric because of free swapping in of Summon Nature's Ally spells, reasonable combat ability (3/4 BAB, d8 HD, not terrible armor, buff spells), and their selections of durable spells, such as Produce Flame and Call Lightning.
For the Archivist play to their skills and their Dark Knowledge ability. Throw in a fair number of the types of enemies Dark Knowledge helps against, and they should feel pretty useful.
Best Answer
The typical approach that I have used and played under is this:
Tier-4 classes can gestalt with tier-5 classes
Tier-3 classes can gestalt with tier-6 classes (i.e. non-adept NPC classes)
Tier-2 and tier-1 classes cannot gestalt
It’s not perfect, but it seems to work pretty well. The higher-tier classes are still more powerful, even with these benefits, but the lower-tier classes are much more interesting than they usually are, giving players more incentive to play them and more reward, in terms of fun, for doing so. My current character is a smorgasbord of monk, paladin, and spellthief, and I’m having a lot more fun than I would as a wizard, even though the guy who is playing a wizard can ultimately do a lot more than I can.
As for distinguishing between classes, the tier list itself covers most classes, and why each class is in its tier explains how to eyeball other classes.
Tier 1 and 2 are relatively easy to adjudicate: if a class has access to something at most levels that trivializes problems in an overpowered or broken way, it’s tier 1 or 2. If it doesn’t, then it’s not. Generally, this means full-casting: a spell progression that eventually hits 9ths. The cleric, druid, and sor/wiz lists have many, many entries that fit this description. The shugenja and wu jen lists are not quite at that level, but probably have enough. And artificer flies here just because his crafting means he can use any and all of the above, if he’s careful.
It’s important to note that tiers should be level- and optimization-agnostic. A broken 20th-level capstone won’t change the tier of an otherwise-fine (or otherwise-awful) class.1 A particularly broken build that manages to break the game with some shenanigans doesn’t count either.2 The idea is that something about the class itself is, at most levels, overpowered.
The difference between tier 1 and tier 2 is, basically, the difference between prepared and spontaneous spellcasting: can the class change what it’s doing regularly, so that it can cover all sorts of very-different situations, or does it get locked into one set of abilities that, while extremely powerful, leave some room for flaws and vulnerabilities?
The other tiers are somewhat fuzzier. Tier 3 is defined as being excellent at one thing and reasonably competent at other things (e.g. warblade), or being quite good at a lot of things (e.g. bard). Tier 4 is decent, or even great at one thing, but useless outside it (e.g. barbarian), or OK at a lot of things but struggles to excel (e.g. rogue). Tier 5 is OK at their specialty, but not even the best at that and utterly useless outside it (e.g. fighter), or is just so spread out that it struggles to get much done (e.g. monk). Tier 6 is NPC classes (and the Complete Warrior samurai, which is basically a fighter with his feats pre-chosen, and chosen poorly). The truenamer doesn’t get a tier, since it doesn’t even work without a lot of work (a high-optimization truenamer probably functions around tier 4 or 5 in a mid-optimization group).
cf. truenamer, who goes from nigh-unplayable to quite-possibly the most inherently-powerful class in the game when he dings 20th.
cf. Pun-pun’s use of ex-paladin