If you have the budget for it, I highly recommend a digital SLR camera in the mid-tier "prosumer" range. Currently, that's the Pentax K-5, Nikon D7000, Canon 60D, and similar. The brand isn't really important from this point of view, although you may want to compare lens lineups. Read this earlier answer on Are there disadvantages to a prosumer camera for a beginner, aside from cost? for details, but the basic point is that these models have controls designed to be used easily. They don't necessarily let you do much more than what you could do with a lower-end model, but what they do offer is dials and buttons that control every important option directly and individually. This is far superior than having the same things buried several clicks deep in a menu.

Of course, this assumes a non-trivial outlay of money. And you'll probably want to budget an equal amount for lenses (and a flash) within the first year or two. That may be more than you want to jump in with, but if you do end up being serious about photography, you will not regret it. And the higher initial investment may even save money overall (note: link is fictionalized).

If you do feel more comfortable starting at lower price point, a high-end point and shoot like the Canon S95 (or whatever is current) will give you a lot of flexibility and be a good starting point. But you probably won't be completely satisfied with it very long. On the other hand, a Canon P&S camera will let you run CHDK, an open source firmware hack which could open up a lot of possibilities in line with your field of image processing and computer vision — if you don't get enough of that in your day (and night, knowing grad students) job.