Yes, the answers provided here are excellent.
My advice to you is to definitly go for the X360 Premium package, the more expensive one. At first, it seems more expensive, but in the long term, it will work out better and cheaper. It will last a good 4-5 years, at least - before the 'next generation' arrives.
The original XBox is starting to become outdated (it has more or less reached the end of its lifecycle) and you can only play the original XBOX games on the premium X-Box 360 console, not the core system (because of the extra memory needed).
Hope that helps.