Prime lenses in only have one focal length. e.g. 50mm, 85mm, etc. Usually their apertures are quite big, optics wise i think primes are usually very good (IMO). But many times, you may find them a hassle as you need to change lenses quite often for diff shooting needs.
Some ppl enjoy manual focus. I prefer auto focus as i am lazy. If you get D40, the 50 F1.8 prime u will need to manual focus.
A bit out topic. But I was thinking, at this budget, why don't you just get a prosumer camera? IMO, it is necessary to hav some knowledge about camera handling and some tech stuff b4 going into dSLRs. You can still keep the prosumer after you decided to get a dSLR later on. I use a prosumer for video recording and travelling too. dSLR sometimes are just too heavy (somemore u find e500 heavy). Prosumers can do much more at a much lower price, but of cause, at an expense of image quality (but many prosumers out there can make gd quality pics too, depending on which one you buying). Good luck for ur exams.
BTW, i'm in NTU too. Stress month.