Purchasing an xbox live kit is unnessesary. All you need is a plain-old network cable to go from your xbox to your router. Any straight network cable will do (not a cross-over cable), because you have a router. Hope this helps. As a suggestion, I would suggest finding everything you need to do the mod(the game and other things) first, as the xbox will be an easy find.
And yes, it is my experience that any xbox modification will get you kicked off xbox live unless you can cloak the mods. Basically you need a mod-chip that can be disabled and all extra files to be placed on a separate partition. One chip that I have worked with that does this nicely is the xecuter 3.