Having just gone through what you're considering going through I was happy to see that I might be able to help someone who might be in my position.
Our greek week is very similar to what you're describing though it went more like:
I. Visit all the chapters out of 5 (general information session)-pef your top 4 and they pref you.
II. Visit the top 4, if you got asked back to them (philanthropy info session)- pref your top 3
III. Go to your top 3, if you got asked back- pref two in order of what you want (or just put one), next day is Bid Day
I had a job interview the first night so I had to do an accelerated schedule on day II to see all 5 sororities. Then I was forced to narrow it down to 3 (that really sucked). I remember that day I was
positive of who I wanted. I had gone to Pi Phi but the girl who I talked to really was not much of a conversationalist, and even though my advisor/friend was a Pi Phi who wrote a letter of recomendation for me, I did not feel the connection. So I prefed the other sorority first and put Pi Phi third. I'm glad I kept them on my list.
The next day I did not get asked back to the one I thought I had made such a strong connection with. I was devestated, but decided to visit Pi Phi again. They totally turned me around. I loved hanging out with them and remembered thinking over and over to myself "this is so much fun" and "I could totally see myself being friends with these girls."
Being overly involved, I spent a good deal of time with my Rho Chi talking over whether I should bid. I did not want to commit and have to back out but when it came down to it, my Rho Co helped me realize that I loved the organization, what greek life can give you, and the girls I had met. So utilize your Rho Chi if you aren't 100% sure because they've been trained to help you make a decision one way or another.
Another tip I can give you is one my advisor gave me. Write up a list of pros and cons for joining a sorority. Look over that list as you go through recruitment as sometimes you can get caught up in the moment and forget why you have decided to become apart of Greek Life. It helped me a lot in decided to become a Pi Phi and made me proud to know I had made an educated decision and not one made just "caught up in the moment."
I hope this helps!