Bzaro can fit the caster slot IF you can get him into a fight to learn the arch afflictor class. Plague wind is broken as fuck, thanks to the AI wasting all its time healing random unimportant status ailments and minor damage. This is how I blew through the second Arena Tourney on my first attempt. Until that point, the healing classes he starts with are his best option, since he gets the best holy nuke with those and you end up fighting a LOT of demons at that point in the game. And you want him to be useful, because getting his trophy means you are going to be spending a lot of time using him. When leveling him in melee classes, make the kiwi skillset his secondary. The boomerang shit alone is worth it, since it can break up formations or instagib enemies who linger too close to high cliffs and lava (the bandit girl is great for this too).
In general, any damage dealer wants dual wield first, attack expert (or similar ones) second, and (if able) bat form to get into back shot positions. Not having to walk around enemies to just appear in the back arc of enemy casters or to simply get to hard to reach places is beyond valuable. The life leech thing stinks after the early game (dual Blood Axes do the job better and work as an end game weapon), so don't bother with that one. The lucky passive from Gambler is great in a pinch if you lack any of the mainstays, since it cuts down on backfire rates of attacks that have them and greatly amplifies critical rates. Depending on build, Equip All sometimes is good, especially if it lets you slap Blood Axes on an a class with otherwise shitty weapon options.
Addressing other specific questions:
Rangers- Dual Wield Blood Axe Rangers are much more potent, because they basically full heal themselves in one round of combat and Ranger is one of the few classes with innate access to Axes. Having said that, simply having gunners makes the AI advance on you more, which is useful.
Princess Sorcerer- Blood Magic, Mind Plus (Hallowed Body is better), and the passive that lets mana take damage are essential. Double Cast Lay waste is basically face roll mode in this game (except the final battle) if you can manage healing the character well between nukes. Thorns counter on the enemies (the computer LOVES to do this) can make this tricky, so sometimes just healing yourself after a single nuke (or Nuke, Quicken, Heal, Nuke) is better tactically. Keeping the computer wounded will make it spend time healing more than hurting you and you are not going to broom an entire map with a double nuke after the midgame, anyhow.
Andeline- Dual Blood Axes, Demon Knight, and whatever attack passives paired with Templar (for self re-res) makes her basically an unstoppable killing machine. Just don't let her get charmed or you are fucked LOL. Knight is decent, too, because the Taunt skill lands on a lot of shit that is immune to Charm, letting her work as a sort of poor man's crowd control. Case in point, Berzerking enemy wizards is fun and they generally suck at resisting it. I considered her good, mostly due to Axes being a core weapon (dual Blood Axe again), but once you start getting most people with dual wield there are better options (Princess Vampires being the most obvious example) for dealing damage without getting flattened by the computer. Andeline has a bit of a glass jaw at times. That said, she is the strongest of the Story Characters aside from MAYBE a properly configured caster Bzaro.
Reiner- Don't underestimate Gambler. He is good with that class and can serve as a melee guy and buffer utility dude ESPECIALLY once you get his personal class. Endgame, he holds up better than most of the story characters and he is the only one who gets a movement ability like Bat Form.
Kyrie- Her personal class stinks because its basically a warmage lite, but as a story character she lacks access to any of the classes that make either casting or hybrids work and her base class cannot equip most of the critical gear that can make hybrids viable. No Vampire class for stat growth and getting around, no Princess for double cast or equip all, no Lich for early life casting tactics. She basically stinks, outside of having higher base stats. I personally set her up as a dual wielder with gadgeteering for utility, having her guard the wizards or providing close in support for my main damage dealers. Once you see what a Lord/Warmage is capable of even WITHOUT dual wield, you will probably give up on her too. She is ok up until midgame, but she starts really falling behind your customs to the point of uselessness. Plus, the bonuses to AP for keeping her from dying are substantial, so its dumb to put her in harms way. If you really want to fight with her, she makes a decent Templar Knight combo, but then again so does literally anyone.
As for what to take, this game is thankfully deep enough that there is no one best party. A lot depends on if the bonus bee or kiwi guys are there to kill, if you are fighting things with lots of magic resistance, or the murder orc woman of doom is part of the enemy group. But there are some basics that it helps to cover and you seem to have a good grasp on that. If you are looking for a solid buffer, that will change depending on side skills. But in general, gambling or gadgeteer let anyone fill in nicely as buffer/utility types. Having two people with those as secondaries is generally enough to cover those bases. You don't want more, because Fellblades start showing up a lot more and the computer loves to spam abilities that strip buffs and hit harder based on the number dispelled. You want solid healing, but this can take numerous forms (mass blood axe dual wield spam, pick any Princess in the group, ect). And the gadgets and gambling often have features that bypass enemy defenses in certain ways. The Club Card for example, seems like shit damage until you realize it ignores any counter and defense stat, meaning its 25-200 will always land and do that range, making it a great way to kill the underground giant wurms in the early game when you are not at the attack cap yet. The spade card of random debuffs will make the computer stop and correct the damage no matter what shitty 1-3 debuffs stick. Most of the gadgets work the same way, but with the added bonus of opening the door to a second mana stone access. Also, if Reiner is in the mix, his imitate ability can break the game, particularly if you copy Bzaro's Plague Wind or a mana stone.
There are really only three most haves:
1) Permakill skill- There are enemies who are simply too fucking annoying to allow to be ressed and there are numerous ways to make sure they stay dead (the bandit girl has universal ones that yield crafting drops), ensuring only the more manageable guys get ressed.
2) Charm/Berserk- Sometimes you HAVE to take an enemy out of the fight and charming/berserking them essentially does that. Charming enemy healers is especially hilarious and effective, since the computer will actually burn its own item stock to heal you if given the option. Remember the computer tends to cheat a lot, so the best DPS is usually charmed derps of theirs.
3) Healers- Half of the group AT LEAST should be able to heal or clear bad status without resorting to items. Early on this is less critical, but in the late game just prior to being able to farm mass status immunity items, the computer is relentless at tossing mass damage and status buttfucks at you. Its ALWAYS better to keep someone alive than hang your dick out there to kill an enemy, because by the time you have ressed and healed the dead guy back up you have wasted valuable time. This is especially true once you are at the point of abusing Blood Magic, since your casters will be parked far away from the action and both those wizards and the advance guys will need healing. Caveat: Mass Bloodaxe Spam means one healer is generally enough, but this is not always the situation you will be in.
