For the PS1 Classic, try Chrono Trigger or Chrono Cross... If you haven't played Chrono Trigger yet, get that and skip Chrono Cross until you're a good deal of the way through.
For the PSP game, try Final Fantasy IV: Complete Collection, Star Ocean: First Departure, or Shadow of Destiny.
For the PSP Mini, try Pix'n Love Rush.
Persona 3 FES is up on PSN, if you're still looking for games. PS2 "classic", excellent game.
PS2 games can't be played on a PSP, even if they are on PSN. I don't think Bot has a PS3.