The PSP has been thoroughly owned, and just about every game for it is available somewhere on the internet. Even emulating the PSP is getting pretty good.
That said, the Vita is much nicer for PS1 games, and if your firmware is old enough, you can even convert your old discs yourself for it.
That said, the Vita is much nicer for PS1 games, and if your firmware is old enough, you can even convert your old discs yourself for it.