What criteria do Catholics use to determine if an old testament character prefigures Mary? I was at a Catechetical training seminar in my parish and the presenter on topic of the creed when touching on the Blessed Virgin Mary said that lots and lots of characters prefigure Mary in the old testament.  The same way that lots and lots of characters prefigure Our Lord. 

What the criteria for 'prefigurement' is when it comes to Mary?  Clearly no one was all that great in the OT and still show us some aspect of Jesus.

Also, do only women prefigure Mary?
A few figures come to my mind immediately:


Eve - "mother of all living" (Genesis 3:20)
Sarah - chosen to bear Abraham's special son
Esther - put in a position to strategically influence the king regarding her people
Elizabeth - Mary's cousin and mother of John the Baptist


Of course, no other figure ever had the Holy Spirit overshadow her and conceive the perfect God-man, Christ. However, the parallels between Sarah's and Esther's willingness to do what was called of them (and the miraculous nature of Sarah's old, barren womb being reopened) mimics Mary in some extents.

The similarities between Mary and Elizabeth are more striking - while Elizabeth was obviously not a virgin, there was still a vision of an angel announcing their future offspring (the vision regarding Elizabeth came to her husband - Luke 1).

I can't say for sure if "only women prefigure Mary" - but cannot think of any men who do.