The SOCOM series is pretty quality, though I think they're 3rd person. 3rd person isn't too different, control-wise, from 1st person. Both Red Factions are fairly recommendable. Aside from what's already been mentioned, there aren't really many particularly good FPSes for PS2. But there are a handful pretty good ones.

Black
Call of Duty series
Medal of Honor series
Star Wars Battlefront series
Project Snowblind

TimeSplitters is one of the best though. So you may want to lower your expectations.