Okay, the answer between the Premium and the Elite (The Core system sucks, no HD) is what you have/need. Here are the differences between them-
Premium- Loud runspeed/fans, 20GB HD, normal/HD video out, White Paint
Elite- Quieter runspeed/fans, 120GB HD, normal/HD AND HDMI outs, Black Paint
What they both have- Wireless controller, small remote (for DVDs 'n' such), all cables (plus Elite comes with an HDMI, I believe)
So the choice is really yours, to be honest. If you're going to run it with HDMI and use alotta HD space, then go with the Elite, or if the 80-dollar price difference isn't a big deal to you, go with the Elite, but if you're not going to use buku-space on the HD, don't have an HDTV and that 80 bucks'll make a difference, then go with the Premium. I would suggest Elite, though. Plus, one thing to let you guys know from experience, I would go with the wired controllers- they're cheaper, don't need batteries, and the cords are literally 9ft long. Plus they use USB so you can use 'em on your computer for controllers too. Wired FTW.
BTW, I've had my 360 since last April, no problems at all, no 3RLOD or anything like that, except for one really strange bug- every time I turn the console off the time resets to 11/22/2005. Kinda odd/somewhat annoying, but no big deal. Just figured I'd let you guys know, I'm not one to leave things out.