Okay, so I'll respond since I'm a brother and all. (btw, there is a Phi Sigma Pi forum....)
Membership selection is private and cannot be shared with anyone not in the room at the time. My chapter sets a quota every year and there are chapters in our region (ex: UNC-Chapel Hill & ECU) that are very competitive and only let in about 6 brothers every semester. My chapter's quota generally hovers around 15.
My GPA hovers around 3.3 and has since I was an initiate. 3.0 is the minimum required and that's all I can say because again, MS is private. I was already involved in numerous campus orgs before I pledged--but others in my pledge class had not. It really just depends.
Just be yourself. Attend as many events as you can because it shows sincere interest.
The initiation semester is very busy and full of a lot of fun! It's so worth it in the end! My very best friends were in my pledge class.
Here is the link on the public side of the national website that loosely outlines the initiation program.
Yay for Phi Sig! PM me if you have any questions.