There are so many things to consider... and your xbox360 shouldn't be high on that list.
Do you want 5.1 or 6.1 ??
Do you have a preference to brand?
Do you have an HDTV? What inputs does it have? How do you connect your 360?
Do you want to have the receiver do your A/V switching?
A few things I would require to be on my receiver...
- optical inputs. (xbox 360, TV, media PC... if you only plan to use 360 for optical, you'll need the one that all receivers have... but if you want other things on optical, too, you'll obviously need more)
- component video switching (my main receiver doesn't have this, so I have an external component video / coaxial digital port switch unit. If you get one with comp. switching, make sure it has the # of inputs you need. Then again, I prefer the VGA connection anyway which makes this useless for 360 purposes... but other components must be factored here.)
- Independent A/V switching (this lets you switch audio and video sources separately. Example: I want to listen to RADIO while playing a game... assuming you run your xbox360 video output through the receiver)
Hopefully that helps. Those are the main things that come to mind. What you need really depends on what hardware you already have.
Cheers