Not much to add to the really good posts already made but here is something to think about. Right now you have pretty much zero responsibilities outside of yourself. You can do anything. You enlist, you start a life. You may find that life may get in the way of what you want to do later. You may meet someone, get married, have kids, decide to get out....are you still going to go to college? You can always enlist after you graduate from college. You may not be able to easily go back to college after you get out of the Army (assuming that you do not make it a career). Graduating from college first gives you more flexibility for your future and keeps the maximum amount of doors open for you.
I didn't start college till I was 34 (finished when I was 41; a lot of people go to college for seven years...
