A biotic of some sort, probably an adept, and probably Asari, or if possible Quarian. I haven't ever heard of a Quarian biotic, and the ME wiki entry doesn't give any information about the matter, so chances are the option won't be there, but one can hope. Anyway, I've always been attracted to wizard/sorcerer type classes when it's possible to make a combat oriented build (one that's not totally useless late game anyway), and ME biotics are more useful in combat than they really get credit for.
As for adept vs vanguard, I like to have more options available when possible, so even though a vanguard might be more useful for a combat oriented build, I'm going for an adept anyway (this is also why the evoker I'm playing in the D&D Pathfinder campaign I'm in is a wizard instead of a sorcerer).
I also quite like the infiltrator class, so likely I'll be playing either a Salarian or Turian infiltrator as well. Both are pretty badass, so it's a toss-up. Probably leaning towards a Turian. Gotta love them.