360/Elite 

Whatever you do, don't get the core system.  The core has wired controllers, no HDD, and composite output.  The Premium has wireless controller, a 20 gig HDD, and composite/component outputs.  The Elite has wireless controllers, a 120 gig HDD, and HDMI/composite/component outputs.  You should get the Elite if you plan to use XBL alot for downloads (demos are about a gig usually) or if you want true 1080p.  Though, honestly, you can survive with the 20 gigs, and I use component and digital output for a good picture and sound quality. Talk