If you are going Xbox -> Router, just a standard cat5 cable like you would use from a computer to a router is all you need. That's what I have on mine...
If you are having problems connecting, there are some routers that supposedly won't work. I had a Netgear MR314 that wouldn't work, no matter what I did. I swapped with a friend and got a linksys, didn't change anything else, and it worked just fine. Somewhere on the official xbox page, there's a list of routers that work and don't work.
Jeff