The best Playstation emulator that there was, was called Virtual Game Station (VGS), and was originally by a company called Connectix.
It worked extremely well for most PS1 games (and had the added benefit that it could be modified in various ways and allowed an infinite number of saves). I do remember some problems with the FF games, but can't be sure.
It was my sole 'Playstation' until I bought a PS2.
You did need the disks in the mac, though.
Hunt around, you might find a copy somewhere - eBay?
Best of luck!
ADDITIONAL: I have just had a look on Amazon.co.uk, and there seems to be some copies of VGS available (probably used) on there.