how competitive?

You'll have a fair chance at all the houses, it really doesn't matter! Most girls make the connections during rush and not before. If you're from somewhere like California or New York you'll find a couple houses which have a lot of girls from there, and you might feel more comfortable at those. If you're from somewhere really unusual (which is basically anywhere out of the midwest) be prepared to have the same reaction over and over - "oh wow that's cool! Why did you decide to come to Wisconsin?!" That might get annoying after awhile, but that'a the only downside I could think of. It really might help you stand out actually, anything that makes you different from all the other girls will help you be more memorable at the end of the day. Good luck!