Whats The Difference Between Xbox 360 And The Core Model?

There are 3 models of the 360:
Core: $279
Premium: $349
Elite: $449
All 3 will play any 360 game (with the exception of the upcoming Oblivion Expansion pack, which will require a hard drive – see below.)
The Core comes with a wired controller, and a standard cable for your TV.
The Premium comes with a wireless controller, 20GB hard drive, a standard cable and a component cable for your TV.
The Elite is the same as the Premium, but comes with a 120GB hard drive, and adds a HDMI cable. Note: some new Premium models now have a HDMI port like the Elite – check the box. I don’t think these HDMI-enabled Premium boxes include the HDMI cable though.
I would highly recommend the Premium model at the very least. For the extra money, you’re getting an “upgrade” to a wireless controller, the hard drive, and the extra component cable. Purchased separately, this is well over $100 in extras.
In addition, the hard drive can be used to store your save games – but with the Core, you’ll have to purchase a memory card (or hard drive) separately for extra money. Also, without a hard drive, you won’t be able to download games, demos, videos or movies from the 360’s marketplace.
If you have a HDTV, the Premium or Elite models are especially attractive since they include cables required for HD – otherwise you’ll have to purchase them separately if you bought the Core.
As for component vs. HDMI – that’s really up to you. Most of the games on the 360 are 720p or 1080i – which will work fine with the component cable. However, if you plan on downloading videos or movies with your 360, or buying the separate HD-DVD add-on drive for HD movies, you might want to consider the Elite for its larger hard drive (more space to store those movies) or at least look for a Premium unit that has HDMI – especially if your HDTV supports 1080p.