(dont go with cod because it is a waste of time that can be finished in 5 days)
Sandbox games are out becuase its very limited..
not quite sure but id look out for games that require VIP passes
There's Warhawk, which is an older game but one of the system's better additions to the online front. Call of Duty keeps mostly the same experience around its pack of shooters, but there are some good games in there, including Call of Duty: Modern Warfare 2 (if you're looking for something specific).
Borderlands is all right, as far as role-playing games go. While the game might not blow the roof off, it's not the worst foundation that you could be dealing with either. MotorStorm and the Resistance series are a couple of other online games that come to mind. If you like beauty or just some fun, get behind the wheel or crawl up behind your blaster for the defense of humanity's civilization.