Joining military to pay for college?

I'm looking into joining the military to pay for college. I used to be in AFROTC, but I quit because they said I wouldn't get a scholarship with there being too many people in the program. I thought I'd be a "minority" being a woman of Latin American heritage as a US Citizen... Anyways... So, I applied for an Army ROTC scholarship, but was not given one due to budget cuts in the US military as military scholarship availability were cut; I did qualify for a 4 year Army ROTC scholarship, though. I'm willing to do almost anything, even enlist... but I want to be able to continue my education continuously, without taking a significant amount of time (more than 3 months) off from college. I'm on the pre-med track, if that means anything... So.. what would be my best bet? My preference for military is: 1- Air Force, 2- Army, 3- Navy, 4- Coast Guard, 5- Marines.