DQ8 isn't on the PSP it's for the PS2 you can get that or Arc the lad Twilight of the Spirits if you want something cheap, FFX if you already haven't played it.

JKTrix was right telling you about The World Ends With You. You can also go with Valkyrie Profile Lenneth for the PSP and FF Tactics if you don't already have it.

For PS1 games I guess you could go with Threads of Fate, Tekken 3 probably isn't as fun anymore with the new gen of fighters, let's see ummm... of you could also go with any of the old ports of the old school FFs.