I did go through Recruitment at Richmond this past January, and I did go Pi Phi.
To answer your questions:
No, you don't need references. I'm the first person in my family ever to be involved with Greek Life, and I know the same went for a lot of girls who I went through Recruitment with.
I didn't really find it super super competitive. The advantage to UR's rush is that it's deferred. Because Richmond is such a small school, you can easily know people in all six sororities before January even rolls around. And everyone I've ever met is super friendly, so you'll get a nice mix of familiar faces to smile at and new people to say hi to even after you pledge. In fact, I ran into two girls that graduated this past year (who I met during recruitment at one of the sororities I went back to for a few nights) while working at the Gap this summer. They came up to me, and we had a nice little conversation.
Here is the link to my rush thread from January (
http://greekchat.com/gcforums/showth...threadid=45214). If you have any questions, feel free to PM me