Using the lore as a 'build guide' actually helps with this sort of thing.
Case in point? Asari Adepts/Vanguards - give them the Disciple shotgun, which is the weapon of choice for Justicars/Asari Commandos.
Gameplay-wise, it's ultra-light, really accurate, and has a great rate of fire for a shotgun. Perfect for Vanguards, but not too shabby in the hands of an Adept, either.
Same goes for the Phaeston for Turian Sentinels, and the Graal Spike Thrower for Krogan Soldiers - they're surprisingly well-suited to their respective races. It's almost like the game was ....designed that way (perish the thought!)...