what good Competitive Multiplayer to buy?

CSS or CS GO in the summer. You could also try DOTA 2 which is in beta, but is pretty easy to get a beta key.

If you're into Mobo's League of legends is alot of fun. could also try tribes ascend but not sure about graphic requirement. or there's also TF2 and as stated above counterstrike.

try out starcraft II, and tribes ascend

League of Legends, Starcraft II.

Modern Warfare 3. Nuff said.

If you are willing to learn and train your skills, I recommend you Starcraft 2.

You cannot get a better competitive game than that.