The other posters have it right here:
Get a relatively nice desktop (build your own!) with a decent CRT (or LCD, if you prefer). MOST of your work will be done at your desk, in your room. You'll have relatively fast broadband, so SSH will let you send your work to any server you wish (if you're programming something that would need server CPU time). Plus, you'll want a REAL keyboard and a REAL monitor--99% of the people that I know that solely have laptops end up buying docking stations or at least plug up a keyboard when they want to do serious work.
If the $$ is available, I would pick up a cheap laptop as well (I've seen some nice Dell specials here recently). As much as you don't like it, you WILL be in the library.... and a lot of major colleges have wireless in their libraries. Plus, a laptop is REALLY nice for group meetings--you can all meet in a central location (that's not someone's cramped room). But you won't be taking notes on it (I've met VERY few people who can actually keep up that way). Security is an issue, though.... my old roommate (back in undergrad days) screwed a lockbox to the bottom of his desk (which seemed to work well).
Best of luck to you!