From my own experience, it seems that basic training and tech school will provide you with plenty of interesting activity, and the idea of collecting and juggling payments on even more credit cards will probably be the last thing on your mind.
Consider that you are already way ahead of the game, as the majority of new recruits will not possess even one card.
Also - if you can wait, you will find that being in the military creates outstanding opportunities to expand your credit profile, as creditors like the stable paycheck that the service provides. (This is also where those who are new to the sudden availability of credit, get themselves into deep financial trouble - but that is not your problem).
By the time you are done with Basic and AIT, a host of new credit products will be available, as the competition for new customers is fierce, and the credit grantors are in a constant race for market share.
For now, just focus on getting through your training - Good Luck !!!