I'm not big into fighting games, but as far as the action games go, I really like Prince of Persia '08. It gets a lot of crap for whatever reason, but I think you can generally find it for $20, and I'd say it's definitely worth it. I also got PoP Forgotten Sands, and that too is a fun game. And if you like the style of the PoP games, all three Tomb Raider games for the 360 are similar in gameplay and pretty fun too.
Otherwise, when I look through my list of 360 games, I guess they're all mostly shooters. :\ In any case, good luck finding some good games!