Her and her (twin) sister, Katie Crutchfield, started out as teenagers in a pretty good rock band called P.S. Elliot. They eventually moved to different towns and split up, with Katie taking a more Singer-songwriter approach for Waxahatchee, and Allison going more indie-rock.
Both are talented, both worth listening to depending on what you're in the mood for. For Allison’s music, I would start with her newest album first as it is more polished though her EP has a couple of good songs.
Sounds like: A good alt-rock singer with some pop and punk influences.