Just came back from Atsugi earlier this year.
Unless your wife really wants quick (i.e. next-door) access to the wives' club, LIVE OFF BASE. It will force you to get out and see more of Japan, and as an O-3/4 w/ deps, you'll probably make $800+ tax-free per month more (Increased COLA off-base and utilities allowance is huge). We lived off-base with my kid who was 2 mos to 3 yrs old during our tour - no issues.
Amazon Prime is your friend. You can also get clothes online from a lot of retailers, and they will come with a free package for any necessary returns.
You won't be able to buy a car until you have a license, and that takes at least a week. You have to take AOB/ICR and the driving class. I don't know which banks are on Sasebo, but you can either take a few hundred bucks out every day from the ATM or have your bank send you money to the local bank. There's no need to bring a wad of G's across the Pacific with you. USAA Debit cards will work (usually) at 7-11, and some of the western banks in the big cities.
The 50Hz/electric clock thing is a little dated. Most clocks use a DC digital timer these days, but it could be an issue. More of an issue is the 100V, which makes U.S. vacuums, toasters, and hair-dryers weak. The base appliance folks should give you a transformer.
We found it was worth paying $2-3k for a solid car for the family. Even if you junk it after the tour, you've just spent $100/month for a rental - not too shabby. There are $500 cars to be found, but they often have $1000 headaches waiting to happen.
Oh ... almost forgot... don't let your wife go to any oriental rug auctions while you're at sea.