I'll copy & paste what I told Sypherz as it will be useful to you.
When purchasing an xbox 360, you should only purchase a slim console, all the other ones are prone to red rings of death. The slim consoles come with a 4gb built in hdd chip, this is not the same as a hard drive. Official xbox hard drives are required if you plan on downloading content/installing games (4gb will fill up after 1 install) or if you plan on playing original xbox games. The official xbox hard drives have a backwards compatibility partition on them that allows them to play original xbox games. The built in hdd chip doesn't come with this on it, as it wouldn't fit. It already has about 0.9 gb of it taken up with configurations and settings. Instead of purchasing a giant modern slim hard drive (I think you can only purchase 320 gb ones that are official xbox) you should pick up an old one. You can purchase a 20 gb old xbox 360 hard drive for around $20. It comes in a case that, with the old chunky xbox's you could clip onto the xbox and it would register. Not many people know it, but if you take the casing off the old hard drives, it will reveal a small slim hard drive that you can use in your xbox 360 slim console. I recommend you get a 20 gb old hard drive and do this, 20 gb is plenty. If you plan on doing lots of downloading you should just do what I do. Instead of spending an arm and a leg purchasing a giant xbox hard drive you could just use an external one, you could pick up probably a 2 Tb external for the same price as a 320 gb xbox 360 harddrive. I use my external for music and movies as well as having a bit of it allotted for downloaded content. It works well for me. Just be careful though, back up your existing files from the external hdd first because the xbox 360 must format it at the start, to alter it slightly to FAT32 format. Don't worry though, it still works with the PC and other devices fine.