Been a while since I've played, so some of this might've changed in the interim. Mostly setting aside resolve damage/charmer, because think it got an overhaul while I was gone. Of what's left, Thief is the best. There are a few factors that go into this.
One is party dynamics. As a general rule of thumb, in a party based game, increasing your own defense increases your own survivability. Increasing your offense increases everyone's survivability. The sooner things are dead, the less time they have to dish out the pain. While CoC II does a pretty good job of making room for one support, the offense dynamic is still in play, and you'll generally want to avoid doubling up on healers*. Since the PC can be anything to start with, while companions will take time to get alternate sets, it's best to play offense for the most party flexibility.
Offense is better than defense, which brings us to the next point: which is better at offense, magic or martial ability? Martial wins hands down. The first reason is that everyone gets the default attack skill, but martials improve it a lot more than magical types do, beefing up the default at will ability. The second is power selection. Martial abilities have big +attack power modifiers. Magic abilities are mostly just the thing without a modifier. IIRC they're more likely to have debuffs, but debuffs are pretty minor for the most part, and dead will always be the best debuff. The final factor is weapon-based damage types. If something resists fire, you're out of luck with your fireball. If something resists your weapon damage type, you can swap to something else as a free action in combat no sweat. You can even use a weapon with resolve damage, getting those nice +attack power abilities and switching out if something is immune.
Gonna run through all the non-charmer level 1 class perks (because they're the most impactful and I'm lazy). Perks are the only class unique thing**, so they're what make or break a class in my opinion.
- Warrior: Terrible. Threat is unreliable, and you know what else generates more threat? Doing more damage, like thief. Also pushes players towards heavy armor, which has too steep a penalty to really be worth it imo; initiative is too important to tear possibly multiple -5 chunks out of it.
- Thief: Fantastic. This is why thief is best. Boosts martial offense, the best thing around. Also makes for tons of synergy with your party. If they can debuff, you can take advantage of that.
- White Mage: Solid. While not The One True Strategy™ of martial offense, support is still plenty solid in this game, and this can really boost your healing action economy.
- Black Mage: Needs improvement. Boosting offense is nice and thematic, but this is pretty weak. At the current point in the game (level 6 I believe), it can barely beat out the thief level 3 sleep perk. Additionally, it doesn't really have a very noticeable effect, in part due to it being such a small bonus. White mage bonus is obvious in play. You got healed even though you healed someone else! Thief is a big enough bonus to be noticeably more damage. Warrior is still terrible though.
All that's why thief is the best class, possibly discounting charmer since I dunno how the new resolve mechanics play out.
*While the whole doubling up issue has had a big step forward with more alternate gear for npcs, think there's still an issue with summoners (assuming a designer imposed limitation rather than an engine one). Not sure if Berwyn gets a different set, and Etheryn is weak and her set comes pretty far along in the game. Summoner npcs work terribly with summoner pcs, because you can only have one summon at a time. In theory, summoner npcs with their summon are balanced against other npcs, and pc summon skills are balanced against other skills/builds they could use. If that's the case, it shouldn't break things to allow multiple summons. Even if it is a bit stronger than other options, I still think it should be allowed. It's like the no combat advantage transformatives thing; players shouldn't feel forced into an rp decision for mechanical benefit.
**Attribute affinities might be argued to be a class thing, but mostly I'm including this as a bonus rant because they bug me: attribute affinities are silly and should be removed. They don't meaningfully affect gameplay. You can retrain your attributes at a cost that's not too steep, IIIRC. New players won't know that though. In fact, they get hit twice by this mechanic, because attribute affinities are one of the first mechanics brought up in game text, increasing the initial hurdle of getting into the game. It's also tied to race, leading to a (very minor) potential case of roleplaying being sacrificed for mechanic reasons. But all of those issues are fine, because in return players get... nothing. Either affinities aren't an issue at all, or you deal with the irritation/tedium of retraining them (if you know you can do that). They don't enhance gameplay in any way.