I agree with spekkio, however if you're already planning to get married then I would do it before joining. I was already married when I joined, and got paid BAH and FSA starting from day one of boot camp. Being from CA my BAH was around $1,700 a month plus about $300 a month for FSA, and that's on top of the E3 pay you get for being a nuke. Just makes sense to start getting that money sooner if getting married is going to happen anyway.
As far as the paperwork, they take care of most of that in boot camp. He just needs to take copies of everything (marriage certificate, yours and his SS cards, drivers license or ID, etc...) with him to boot camp. Your soon-to-be husband just has to make sure that DEERS has all your information right, and that you're listed as his dependent. As mentioned before, once he gets over here to Goose Creek, he'll get the choice of either going back home to do a DITTY move (DIY, and getting reimbursed) and bring you out, or doing a NAVY move, which is just where they send movers out to your place to bring your stuff to Goose Creek. He'll also have the choice of getting a house here on base (and no BAH) or receiving BAH to pay for a place off base.