Joe,
Pro/E, Solidworks and Inventor are all available to FIRST teams for free, so selecting one is a matter of preference. Your bias against Pro/E for FIRST use is, barring any external pressures, warranted -- in my opinion. It is the least friendly of the three packages to work with and doesn't offer anything particularly useful.
Inventor is popular since it's been available to FIRST teams longest. I don't like it and it is not used in industry much, so if you're interested in giving your kids a marketable skill, it's a bad choice.
Solidworks is what I use for my team (and professionally) and we were able to secure 25 licenses by filling out this form --
http://www.surveymonkey.com/s.asp?u=91132550276
There is good support among the FIRST community for both Inventor and Solidworks with respect to available KoP models and people who know what they're doing to help you out.