From what i can see, Perception, intellect and resolve are the big ones, but I don't know how much they overlap/are necessary. Ignoring combat prowess, what class(es) would be good for having lots of delicious dialogue options?

As far as i know most dialogue options require high perception/intelligence/resolve. With that in mind:

 

Currently i believe a melee chanter tank/summoner would be a really good choice since you need to put most of your points on int resolve and perception. It is a fun build and works quite well. Stat choices should be similar to this : 8 Might 10 Cons. 8 Dex 18 Per. 16 Int 18 Res.

 

Also a tanky wizard can be a good option, but i haven't tested it yet. You'll probably want lots of buff and debuff spells since you'll have low might (e.g level 6 spells gaze of the adragan that petrifies the enemy (the best debuff effect in the game along with paralyze), and citzal's martial power that makes you a really strong fighter for 20+ seconds)

 

Lastly a melee tanky priest with similar stats to that chanter above will work great imo. But again you'll want to use buffs and debuffs only, since you'll probably sacrifice your might stat to gain high int/resolve/perception.