1) F1
2) H1B >F1
3) F1 generally not allowed to work
4) H1B can go school as long as you work full time.
5) H1B need work to keep your status, in the mean time if u have time u can go school (without the F1 or I20. ).
6) get your H1B and if u not get your degree yet, you can finish your thesis/desertation while you are full time working.
7) so just forget about F1 and I20 if your had got H1B