Ask for their rank (what they are called in military terms - different branches use different terms for the same pay grade), pay grade(what they are paid)- you can google it - it's public info, specialty (what job they actually do), Contact information for their unit Commander, in addition to their immediate supervisor.
Do some google research - don't get confused with rank sounding the same as position. Especially in the navy. Example: A Commander is a rank, this person is not necessarily the one in charge of everybody. But they also call the person in charge of everybody Commander. You should be able to find out online whether the name given as unit commander really is, since that is the big cheese. This is the person you contact (in addition to the immediate supervisor)to report misbehavior by the tenant. They do not want to be bothered and find out their underling is not behaving well in the community - reflecting poorly on their branch of the military. This person can cause trouble with their career by putting an official disciplinary action against them.
A military base will often have a dedicated phone prefix and zip code. Google will help you verify what that should be and match it to info given for the supervisor/commander.
Get a copy of their LES - Leave and Earning Statement - that shows their income.
Also get a copy of their orders. PCS means Permanent Change of Station - moving to a new base. If they say they don't have a copy, call BS - you get LOTS of copies & know they should have plenty available for everyone who asks.
If they are separating from (getting out of) the military, get a copy of their "Form DD214" - the discharge paper that shows their entry and separation dates, as well as what type of discharge they got. You (I)want only Honorably discharged. You can have some discipline issues and still be honorably discharged. You do NOT want someone with who was so bad they got a general or dishonorable discharge.
A medical discharge is up to you. That means they will be receiving financial benefits - you will not know what type of physical or mental impairment they may have, or if they just said "OW!" at the right time, to fake an injury & receive benefits - happens all the time (I used to work with someone who bragged about it - disgusted me). They can still be fully employed, or not.
After they arrive, at some point, they may claim that they are breaking your lease to move into base housing. This is true - if housing is not available at first, but becomes available later, they must be allowed to go without penalty. BUT- confirm it. They should have orders, and they may also lie about it to get out of the lease. Also, you need to get normal notice to see if you can find another tenant.
Screen everything else as usual: debt-to-income, credit, attitude, cleanliness, etc.
You might Skype them from home, to get an idea of how they live/clean. But, they might not cooperate (or show you a friend's home), not show the dog's dishes - or the dog, and you can't smell it. Better to hire a local real estate agent to property manager to go over & smell as well as see their current place.