For a crowded campus, and an inexperienced rider, the slower/slacker steering geometry of a mountain bike is probably the better choice, but it does exact a penalty. They tend to be heavier and slower than a road bike. If the commute is over a mile or two, a hybrid is probably the better choice....better gearing along with higher pressure tires and larger diameter wheels which give a touch better top end and easier pedaling and they tend to be lighter frames if you're careful in your purchase.
But a road bike under an experienced rider would be much better, albeit you'd have to deal with the faster/twitchier steering geometry of the road bike....and provided it's set up for commuting rather than pure road riding.....like this:
Flat/riser handlebar which sits you more upright so control is a tad better. Add in wider tires, like 32's instead of the typical roadie 23/25's, and it works much better for longer commutes.
I used that bike above for years commuting around my local university's campus after suffering through a few mountain bikes. But my commute was just over 5 miles, so a mountain bike, even with high pressure slicks (which adding those to a mountain bike completely negates any off road argument that can be made for a mountain bike....) the higher weight and slower steering made mtn. bikes just too much work.
To the OP....I'd look into mountain bikes if I had to, but I'd look for a higher line Trek than an 800. That particular Trek was their absolute bottom end and the frame is especially heavy....while it had a cromoly seat tube, the rest of the frame was made with heavier and lower quality hi-tensile steel. Look for at least a Trek 820 to move to a complete cro-mo frame....it'll be a tad lighter and more durable.
As for high pressure slicks on a mtn. bike, there really are no high pressure slicks made any longer for them. Continental used to make a set based on their high end road bike tires that were rated for 100 psi, but they were sold in such low numbers Conti ceased production of them. These days, 60 psi is now the "high pressure" slick....and almost not worth spending the bucks on them for a marginal decrease in rolling resistance you'd get, not to mention---again---the fact you'd lose any off road ability, just like with a road bike.
A hybrid with 700C tires, 32 wide, with a slightly knobby tread, would most likely be the best compromise for school commuting.