I started with Half Life, Quake, Unreal Tournament and Medal of Honor way back when. What got me into the FPS scene most, however, was Counter Strike. As much as I love the story of Half Life, gameplay of Quake and UT, and the online play of Medal of Honor I'm still playing CS today (well, CS: Source, but it's practically the same thing but easier) 7-8ish years later.
Play Half Life, one of the Call of Duty games, and buy the Orange Box and you will be have a good general knowledge of FPS's but play CS and you will become an addict.