Soldier of Fortune II...not a deep game, but very fun. The Operative: No One Lives Forever. No One Lives Forever 2...both very fun games. Jedi Knight II and Jedi Academy....the FPS experience isn't so great, but when you get the Light Sabers the fun begins. Call of Duty GOTYE this is one of the best FPS games I have ever played...I absolutely loved it. Halo 1 is pretty good when you are outdoors, but the indoor environments are exactly the same every time you turn a corner and it gets boring. Splinter Cell and Splinter Cell Pandora Tomorrow are third person...as are Max Payne and Max Payne 2 and Hitman 2 Silent Assassin...but I loved all of these games.
All of these games play well on my P4 1.9Ghz 256MB RDRAM Geforce 3 Ti 200...so I am sure they would run fine on yours.