Having been burned before, do NOT make your own reservations and expect the military to reimburse you unless you FIRST have explicit written authorization to do so. The military's SATO department (scheduled airline travel ofice) will make your official reservations for you, using locked-in contracted government rate arrangements.
Also, you may have difficulty changing your flight dates/times once the reservation is paid for by SATO. You can try, but don't be disappointed if it won't go through especially if it results in a higher charge. Once SATO electronically books and pays for a reservation, it's essentially written in stone. You are, however, allowed to utilize personal frequent flyer miles to upgrade to first class - the law which previously prevented us from doing that on official travel was dropped a few years ago.