I'll reiterate what the previous posters have said: whether you enlist in the Army, Air Farce, Navy or Marines, once you enlist, you become "government property." Your desires, goals, ambitions, needs, wants, etc. take a back seat to the needs of the Army.
While it's true that finishing your degree is encouraged, you will have to do so on your own time, and there is no guarantee that the medical school prerequisites will be available within a close proximity to your base.
The feasibility of taking college courses part-time while in the service has a lot to do with your particular job and schedule, the course schedule at the local University, the current op-tempo, the willingness of your chain of command to help you out, not keep you around after work doing useless bullsh*t, etc, etc.
I am in no way putting down military service; I derived a lot of benefit from my brief stint in the Army, but anyone considering enlistment deserves to have an accurate description of what they are getting into. It has already been mentioned that you would most llikely go to Iraq. I would also add that when you enlist, you do so for eight years, even if you only sign a two year contract. This means that after you have completed your term of enlistment (say, two years) you will be in the Individual Ready Reserve for six more years-in short, you'll be a civilian, for all intents and purposes, but you will be subject to recall to active duty while in the IRR. I'm sure you've heard that many IRR soldiers have already been called back to active duty to go to Iraq.
In short, join the military only if you truly want to be in the military and all that that entails. It would be prudent going in, however, to assume that you won't be able to start your prerequisites until you've completed your active service.
Good Luck