If you've landed yourself an Xbox 360 Core System, then you've been bundled with a stock standard composite AV cable -- that's OK, but it's the lowest quality cable you can hook up your 360 with. If you want your 360 to produce its best, then you need to hook it up to your television using HD-capable gear, such as Joytech's Xbox 360 Digital AV cable.
The Joytech Xbox 360 Digital AV cable features component, S-Video and composite connectors -- the component one being the highest quality choice. It also features a stereo out, as well as a digital optical cable for better audio support (provided you have an amp or receiver with a digital audio input, of course). The cable itself features durable build quality, while its length of roughly 1.5m should suit most home entertainment set-ups.