Welcome to the world of PC gaming. I have to say it all depends on what you want to play there are so many games out there to tell you to look at.
I suggest looking at Steam found here http://www.steampowered.com
You can find tons of games there new and old. I suggest looking at some older FPS you can get them cheap. Unreal Tournament 2004, Half-Life 1/2, Counter Strike, Team Fortress 1/2, Call of Duty (any of them).
I saw someone said to try Battle Field 2/2142 those are great games let me know if you get those.
Those of us here should start a Steam group for SevenForums and trade Battle Field names so we can have some fun there.