One

[Dyne]

Gears definitely. Fable II if you want a lengthier single player I guess, but I would still get Gears 2 and do Coop. What an amazing game.

Also, Banjo doesn't look that bad and it's really cheap, too!

[Typhoid]

I'd say Fable II.
Shooters are always going to be shooters, but if you want to dive deep into a game for days at a time, I'd say get a relative RPG-type game where you can immerse yourself in the entire ambiance.