Glad to see you are already going o go for Team Fortress 2 on PC. HIGHLY recommend it though the only downside is you may not want to play anything else by comparison!
Half Life: Source
it's cheap and is a slightly prettier version of the absolute all time classic PC game and also a great background to Half life 2.
Also Painkiller Gold. Yahtzee's infamous review said as much, but pro tip: learn to bunny-hop.
-Left 4 Dead 1 & 2 (best played with some mates or place to make friends)
-Call of Duty 4 (much better online & enjoy the mouse + fully customisable controls)
-Aliens vs Predator 2000 (re-release on Steam, very good game + cheap as chips)
-CounterStrike: Source (Boiled down essence of online shooters, stick to small player numbers for rapid matches)
-FEAR (the first one but also FEAR2, perfect fusion of Horror, First Person Shooting and Slow-mo mechanics)
-Doom 3 (Long game, kinda repetitive but challenging, scary and visceral)
-Max Payne 1 and 2 (very good games that are almost impossible to play without mouse aim)
-House of the Dead 3 (look for this in bargain bins, a solid light-gun shooter that transitions well to mouse controls, also previous HotD games)
-Duke Nukem 3D from GOG.com
-Resident Evil 5 ( plays so much better on PC and benefits so much from mouse aim)
-Mass Effect (PC version fixes many of the game breaking problems)
-Lost Planet Colonies Edition