XBOX draws verry little power. - You can get a smaller inverter. I dont have an xbox, but I think a 90 watt will do fine. check the specs on the xbox for power requirements.
The best way to power the inverter is to run a line from the batery w/ a fuse to a switch, and then into the trunk - you only need to do this with the hot or + lead. the ground or - lead will go from the inverter to any space of bear metal on the car body.