PS1 owners looking for a great FPS experience shouldn't look any further than Final Doom which was released a few years back.  It's everything the original Doom was, only with new, bigger levels, a lot more enemies, and a lot tougher gameplay.  The only gripes that can be found is that Archville and Spider-Mastermind were not included in this conversion, but the smooth frame rate, gorgeous (for its time) graphics, and challenging gameplay make Final Doom one of the best first person shooters for any system, and is a clear overlooked gem for the good 'ol PS1.