I left Goose creek late in 2001 so some of this will be speculation, but here's my .02
When I was there housing was not the nicest, but it wasn't bad either. It was extremely convenient to school and the commissary. This may be more important to you than you realize. Having a 5 min drive to work becomes significantly shorter than a 20-30 min drive, when you will be making that drive more than 5 days a week, (most likely 7) and wanting to go home and relax after school before night study.
The commissary has become a significant financial advantage provided by the military with the way that food costs are skyrocketing.
There are fenced yards in housing, and you will be able to have your dog there. I have a 45lb "pit mix" that looks nothing like a true pit bull terrier, and I have experienced first hand breed specific exclusion in apt hunting. My friend has lived on two bases with his Rott, without any trouble.
Base housing will pay for electricity/heat/water/garbage, out in town that will come out of your pocket. Housing is also being privatized at bases across the country. A lot of the old structures are being torn down and rebuilt as part of the contracts. My same friend just moved into new housing in Groton, and he and his wife love it.
These are all just things to take in to consideration. I personally have not lived on base since NNPS, but it was not too bad while I was in school.
Your BAH when you arrive as an E-3 will be $1138/mo as per:
http://perdiem.hqda.pentagon.mil/perdiem/bah.htmlCheck craigslist Charleston to get an idea of housing costs.
When you finish bootcamp you will fly from there to Charleston. You will be assigned a barracks, but you should be able to move out immediately. Do not expect time off to move though. The Navy will move your stuff for you. Google smartwebmove to learn about the process. You have two options. The Navy hires a contractor, or you move the stuff, and the Navy pays you ~90% less taxes of what it would have cost them. I have always done the self moves, because it's pretty good money. Either way, your wife is probably going to have to do the brunt of the work because you will be starting school. You can use your initial move at any time though. If you are going to be getting to Charleston shortly before a holiday, you may choose to live minimally for the first month or two, and do your move then. Or if you are going to be a mechanic, it's only a four month a-school until you have a few weeks off. It's really all about the comfort requirements of your wife, since you probably won't be home much.
Good luck
MM1/SS