When is the best time to sign a contract with the military?

Lets say I want to go into the military in the fall after school is over this summer so I can graduate with my masters degree. Is it better to sign now and have a delay in leaving time in a few months or is better if I wait till I officially am finishing and have the masters degree? Which would be more beneficial for me? I want to leave and go in as soon as possible once I graduate. Would waiting to sign till I officially graduate prolong the wait time till I can leave for basic and would it be more beneficial for me to wait monetary wise for when I sign?