Here's the deal. We won't be able to take leave after Basic training. If your school isn't at Lackland, they bus or fly you there after Basic. It is a PCS, but no pay or allowances for moving, they take care of that for you. Once you're at tech school, a car will be worthless for at least the for month or so. After that, I'd try and get some to bring it to you or hope for a holiday that you could fly home and bring the car back. You will get paid mileage when you leave tech school for your first base.
Great choice on joining the AF. I've been in 5 years now and love it. Let me tell you, life is good. Pay is not bad at all, plenty of leave, and great people.
As for the storage, if someone is not going to be driving it, get it on jackstand with plastic underneath it. Also, when someone starts it, have them run the A/C to keep the seals lubbed.