Trem -the cable should come with your 360 as standard... unless you bought the core console without the harddrive? It has an optical out on the port that plugs into the 360.
and no no no no! The best res you can use on your screen is the native res of your screen. So 1920*1080 for you, or 1080(i/p). If you use 720p, then you are feeding your screen a lower res, and then your screen is upscaling that picture back to 1080.
Oh and I looked up your new tv. It does look lovely. Pics!