I'm not an expert on the US military, but I did do 22 years in the Royal Air Force, so I've got a pretty good handle on how military people think! They won't go for your 'you scratch my back...' approach; they want (and can get) people who want nothing else but to fly for Uncle Sam - with all the BS that that implies. If you want to consider going this route, take the time to learn as much as you can about the USAF, its recruiting methods and requirements, and life in the military generally. You'll find lots of info on the web.
As for moving around, as Reddo says, you'll get lots of that as a junior pilot working your way up the civilian ladder - and, unlike the military, your employer(s) won't pay for the moves! And life as a pilot is rough on the family whichever way you go about it; you have to get yourself a partner who understands these things. I'd hazard a guess that the divorce rate in the air force is lower than it is in the airlines, simply because the military tries to look after the whole family even when the breadwinner is away - no civilian employer gives a toss about your family.
Make no mistake, life as a pilot is no easy way out, civilian or military. The rewards can be great, but it's a long, slippery ladder to the flight deck of a heavy airliner in a major airline.
Scroggs