Best FPS I've ever played. It should be pretty cheap now too.
I personally hated HL2, even though I really liked the original. The game just got exceedingly boring as it progressed.
GTA3, VC and SA of course are all excellent. Use the Wingman controller for the driving parts and the mouse to aim and shoot.
Splinter Cell is excellent and best played on PC
Half-Life is a good starter and then you can progress into better graphics.
RTCW is good as well.
NFS: Porsche Unleashed is one of the best values out there. I picked it up for $9 and its a great racing game.
For strategy, I like Civ3 or even Civ2.
That's all I can think of off-hand. Enjoy