I've always sucked at fighting games, but generally speaking I've been playing Melty Blood: Actress Again Current Code for a longggg time.
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When I say a long time, I don't mean I've put a lot of hours into it, although I've put in a few, I just mean in terms of fighting games it's the one I revisit most often. I mainly play C-Ciel, as I like how much she can jump around the stage, and especially that leaping throw she can do, that shit's fun.
I have recently picked up BlazBlue Centralfiction too, and Kagura has been great on that.