[AnchorAlumna]

Actually, in this case I wouldn't worry about getting recs. The sorority will do that, if it's a high priority with them. They would NOT expect you to have recs. If you or your parents know somebody who is a member of the group coming on, then certainly ask if they would write you a rec, which they can send to the group's international headquarters. PM if you like!
As far as dress...it couldn't hurt to dress up a little...like you said, business casual. Neat...well groomed...put yourself in the best light possible!