He would be in the Air Force from his date-of-commission, which he would obtain upon graduation from the Academy. Not all cadets who attend the Academy go on to serve in the military [however, those who do not are liable for repayment of their tuition], and at the cadet's discretion, he or she can request a commission in another service: the classes of the 1970s and early 1980s frequently requested Army commission in protest against Air Force integration policies.

Incidentally, though it is not relevant to Jack's schooldays, with a birthdate of 1952, it is pretty much certain his father served in WW2 or Korea or both. We have no canon on Jack's family, other than that little essay Rick wrote, but I like to think of Jack's father as being Army Air Corps. His mother, of course, could also have been...