You can play most of the Final Fantasy games on the PSP, but No. III has been a bit of a sticking point. One that will be plastered over with the arrival of a cut and shut edition made out of the DS version and the iOS edition.
With a choice of original or updated music, double-speed battles and 16*9 display, it'll be out on both UMD (ideal for importing, as the first two had English built-in) and download at a budget-ish price. Andriasang has some screenshots to tempt you, the game is out in September.