I think first of all you need to decide whether you want to shoot tape or film, as both offer their own challenges. As a student myself I found that an investment in a decent prosumer camera ($1500-$3000) gives you the flexibility to work with more professionally motivated features, without having to drop a ridiculous amount of money off the bat. A big consideration, if you are going the digital route, will be what format you want to shoot in (ie. DV, HDV etc), as well as the tape format itself (or hard drive). If you're looking to learn and not necessarily showcase the work you create on a big scale, then standard definition on MiniDV is a good bet as you can get a better camera for your money (particularly if you buy used). However, given the direction most video work seems to be heading, HD or HDV could be a sound investment towards more professional or artistic work ahead. But if these prices seem a little high, then just look for something that satisfies what controls you would want over an image, but generally as many manual features as possible is good. (Just don't buy a little camcorder that fits into the palm of your hand). Some general suggestions would be a Canon GL1, GL2, XL1, XL2, A1 (HDV), Panasonic DVX100A, DVX100B, as well as some comparable Sony models which I can't recall at the moment. Ultimately, I've found that having a digital cam with a decent lens on it was a great way to learn, and learn cheaply too, given how much a miniDV tape can cost.
But if you want to go the film route then the suggestions above by Toby seem appropriate. Film offers a whole new range of challenges not found with video, but can be a very rewarding experience to work with. But it can also be very pricey, especially if you are looking to learn and experiment. But if you do, then definitely go 16mm, and look for camera kits in the under a $500 range. At this price you will only find used stuff, which is generally a fantastic resource as long as the equipment has been moderately cared for, and try to look for a camera that has a reflex viewing system versus something like a parralex (SP?). Also a few different lenses is always an asset.