I have 1 and 2 modern warfare's wich were sick, for a while, then they just got boring to me. Thats just me though. I really am into the mx vs. atv series and the newest one, Reflex, once you can get good at controlling it, its sick as hell.
The 360 is only backward compatible on certain original games. There's a list somewhere on the internet but I'm too lazy to look it up.
I guess it depends on what kind of games he's into. There are a boatload of good ones out there. If he likes FPS then try Halo. Call of Duty. Bioshock. If he likes racing, then Forza 1, 2 or 3. Plenty of sports with EA and the Madden series. I usually head to ign.com to look at reviews and what's popular. Pretty good gauge of quality.
MW2 MW2 MW2!!! And mw1. Cod5 world at war. Halo 3, 2 , and 1, ummm...baja edge of control. The burnout series are also good games. gears of war 1 and 2 were fun for a while as well.