Str characters are the bread and butter of the dps world - wading in knee deep in blood, they hack and slash with 2h weapons to smash out massive amounts of damage. A few knockdown spells in their repertoire and a charge give them some CC but ultimately it's all about the big hits.
Dex characters offer a lot of support, don't feel trapped into choosing between bows or knives because a smart dex player can bring both. With high speed you'll offer great deployment, excellent CC options and a lot of movement.
Int characters have the most spells available, so they bring more variety than you'll fix into a single build.
Damage - Found in Pyro and Aero heavily
Control - Aero/Hydro are good for locking down the enemy.
Support - Geo/Witch focus on buffs/debuffs.
Str/Dex - Str players will gain movement from the dex, skills to get you around the battlefield quicker to deal more damage to spread out foes. Dex players will gain higher armor, better AoE damage too.
Str/Int - Str players either gain ranged attacks, self buffs/enemy debuffs or the ability to stop the enemy from pounding away on you. Int players get heavier armor, more damage with a 2hander and some additional CC options.
Dex/Int - Dex players get self buffs, or extra control to really dominate the battlefield. Int players can gain movement or maybe a sexy bow option for cheaper ways to play off their own spells.
Whatever you fancy is available, just make sure someone has a healing spell to top you off outside of combat!!!