How long should I run a mile before I ship out?

I barely ran my first mile in 12 minutes. Depending on your age 9-10 minute mile is an acceptable starting point. You'll still be suffering in Basic at that rate, though.
Concentrate on running intervals instead of long slow distance runs. The first one will bring your run times down and keep your workouts short, while too much of the second one will cause overuse injuries.

Six minute miles will give you a good score. Try to get it down to 8.5 if you can. Make sure you hydrate.

When I was Army ROTC, I had to do two miles in 18 mins in fatigues and combat boots, which I finally got, though I sprained an ankle, my run time went back up, I wasn't allowed to go to Ft. Bragg for summer camp...I went USAF OTS instead, there, I had to do a mile and half in 12 mins, I made it with one of my roommates from my first class pacing me, screaming at me and nipping at my heels the whole way, I was then recycled, and had to go through with the next class, I was with the first for nine wks, the second for six wks...I eventually got up to 8 mi a day, in broiling heat in TX, before USAF OTS eventually got moved from Lackland in TX to Maxwell in AL...one guy, amazingly, at USAF OTS had been an NCAA track star, I kid thee not, he did the mile and half in six mins, for real, with this weird, bouncing, gazelle-like trained athletic gait he'd obv been taught...I also do aikido and iaido, which I started later...trust me, 3 hrs of aikido, which is a blend of judo, jujitsu, and kendo, is like running 10 mi, minimum...iaido is more anaerobic, however, equally fatiguing, it's Japanese swordsmanship using either wood blades, or blunted metal blades, one needs a license for a real katana sword, only the highest levels are allowed that, ever, look up US Aikido Federation, or Birankai aikido, the two topics are often taught together, if you'd wanna chat more, just lemme no rush, whenever you'd want that'd be convenient, OK? And I also taught myself controlled exhalation techniques to keep my respiration constant, I got looked at as if I was a weirdo for sounding like a choo-choo train, forcibly exhailing on my every third footfall, however, it had the dubious distinction, as a technique, of actually working, as I've always rather tended toward asthma, I had to develop the technique, however, it did, at the very least, seriously work for me, I'm total perm disabled now....