I also did both during my (final) two year non flying tour: I got my CSEL and CFI through the aero club, then taught part time at a local FBO.
Unless you buy or can find a really good deal on block time, I'd say stay with the aero club. You probably won't be able to beat the price on an hourly rate, and the facilities will generally be nice and the planes well maintained. Sometimes the maintenance at your local mom-and-pop FBO can be less than what you're used to.
On the down side, you'll have to deal with the usual USAF BS of monthly safety meetings and stan/eval tests for every airplane, but for someone just getting into general aviation, that's not entirely a bad thing.
Don't worry about not being current in jets when you get out. I hadn't flown anything bigger than a Beech Duchess for two years when I interviewed, and it wasn't an issue at all.
Good luck,
Z