I've done a ten mile commute on a mountain bike, a hybrid, and a road bike, and they all have their advantages.
Mountain Bike
My mountain bike was rugged enough for dirt paths, but it was heavy and not very fast. That's not as important with a shorter commute like yours, but mine is ten miles, so that gets old. They are handy if you plan on cycling when there is snow.
Hybrid
My hybrid had bigger tires, room for fenders and a rack, plenty of places to clip lights, and was made out of aluminum, so it was light. It was a really happy medium, and totally my favorite (it was stolen). If you plan on cycling in bad weather, or snow, or have to carry things, a bike that can accommodate fenders and a rack on the back will be a huge benefit to you! I work 12 hours and carry a big lunch with me, and it's nice to not have it bumping on my back the whole way in to work.
Road Bike
This is what I use now, since it's the only one I own, and I love it. Road bikes are FAST, and even steel frame ones are pretty lightweight. I picked mine out of the trash and fixed it up (It's from the 70s), and it still runs great. My only complaint is that it's difficult to carry anything because of the lack of a rack and the bent over angle. OH, and they're pretty terrible in snow and wet conditions because of the lack of grip from the thin tires.