I just finished my first (and only) enlistment in the Marines. I don't know how much "softer" the USAF, all macho shit aside, but I assume there is some of the same issues you'll face concerning politics and what I like to call "Military efficiency".
There is no way in hell I would ENLIST at 37. There are too many grown children that will take pleasure in making the old guy do stupid shit. Maybe the AF is different, but we had guys that were in their late 20's and early 30's with college degrees (not dumbasses, honestly really good guys) that got shit on daily because they were a PFC or lance cooly, and the SGT had a point to prove. The only thing you can do is do what you're told, or get shit on worse. Right or wrong, that's how it is. Rank is rank, and you get treated as you rate.
You'll be required to fall in line with the rest of the little 17-19 year old kids out of highschool and you'll get treated just like all of them for a year or possibly more. You may get promoted faster because your work ethic and maturity will be better, but there will be times when the kids get promoted faster than you etc. etc... And it's not like you can get fed up with it. They have your ass for 3+ years.
If you have college, I would go officer and that could maybe work for you at 37 a lot smoother than enlisting. The reserves may also be a decent option. Full-time active duty junior enlisted at 37, however... I would advise against it.