Hard disk is where things like saved games, demos and even whole games are stored. Strictly speaking, you don't need one, but in reality, you want as big as you can get - downloaded demos and such will take up anywhere between 5 - 20 GB (depending on the demo) and save you money since you can try them out before you buy, and I've found some demos are enough and you find you don't need to actually buy the whole game! Installing whole games may well take up even more than that. The benefit of installing a game is mostly the noise - the DVD drive on the Xbox is pretty loud, so if it's not having to constantly read the disc, it saves on noise. It also speeds up loading times, but not by a lot. Also you can store photos, music etc. on there if you fancy.
Not too sure on the editions, I think the Elite is the one to get in terms of ensuring you get everything included, but make sure you get one with an HDMI - it makes things a lot easier than having to connect up the old component cable to get HD, and you can also get surround sound through this without having to hook up the additional optical cable. It also means it's one of the later units which shouldn't be affected by the RROD (red ring of death) issues the very early editions had.
Apart from that, don't think there's anything else too complicated - if you're getting wireless controllers, would suggest getting either the rechargeable battery units or use rechargeable batteries as otherwise you'll go through a lot of normal ones!
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