If you have your 360 hooked up to your TV via an HDMI cable, you should be getting the best possible visuals. The 360 can only display at 720p, so it up-scales the image.
Other than that, I'm not really sure what you mean.
The 360 only renders in 720p, but can output at 1080p (although IMO it's pointless to do so). You should just be able to plug any HDMI cable in (provided you have an HDMI port on your 360) and set the output resolution on the 360 to 1080p or 720p (which is what I do...I don't bother with 1080p with the 360).
Edit:
What is Turtle Beaches?