House of the Dead III might be worth a try!
Apparently it includes the full House of the Dead II game which is unlocked once you complete House of the Dead III! According to IGN it is even a lot of fun with just the gamepad. But if you can get hold of a lightgun for your Xbox, of course that should be best I would think.
Well, I haven't tried it myself yet. I just got me an Xbox lightgun from GameXchange store today, and ordered the game today. I cannot wait to try it though.
There's a surpising amount of very interesting Xbox games that got ignored back in the day because everybody was just focussing on Halo. Especially if you have a decade-old pc that cannot play any 3d games, then I'd say the xbox is a _very_ attractive platform to get into. Right now, the console and the games are insano cheap used.