If you are interested in the NPC (26 sororities that are considered the ‘traditional’ sororities, and 18 have chapters at Michigan), they are competitive but there should be a spot for you (see post #1 above for the complicated system they use).
Those 26 sororities have an agreement as to what sororities are allowed to do and to offer, no matter what campus they are on. No hazing, no alcohol (ever, not even alums) in the house, rush rules, discrimination, etc. Of course there are going to be differences. My niece belongs to the same national organization as I do, and when I asked her about them signing songs she said “Oh no, that’s hazing.” I couldn’t believe it. What some consider hazing others consider fun (singing, doing skits, doing ‘safe ride’ duty on Friday nights).
Sign up for recruitment and just see where it takes you. If you like it, join. If not, find another campus activity you like. It’s just a few days out of your life (usually 2 weekends) to see if it is for you.