I agree that the ferry is a good choice if it's your first visit, and just the two of you. It's much more expensive than taking the public ferry, but it's a special occasion and will make getting there a breeze. Get in line to board the ferry early for both trips if you want to enjoy the sunshine, as there is very limited seating up top.
If it's cold at home, I pack summer clothes in my carryon and change in the airport restroom.
If you plan on drinking at home, stop by the duty-free store at the airport before boarding the bus to get to the marina.
If you arrive at Crown Bay marina early enough, you can stop in the little grocery store there and grab a few snack items/beverages that can tide you over until you make it to a grocery store. (Be prepared for sticker shock!)
If the ferry schedule permits, you can also grab drinks/lunch at Tickles restaurant at the marina, too. Good food and reasonably priced.
If you plan on snorkeling, even if you're just a casual snorkeler, invest in a decent mask and snorkel to bring along. Having good equipment, especially a good sealing mask, will make all the difference. Fins aren't as essential to pack, as you can rent decent cheap ones on island. My husband still hauls his full-size fins and chafe-guard socks everywhere we go because he's part dolphin, but I've switched to the shorter ones.
If you stick to the closest beaches (e.g. Caneel, Trunk Bay, Hawks Nest), you can get by with taxi drivers. Rates are published on VINOW.com. If you want to venture out further (Waterlemon, Coral Bay), then you should rent a car.
Personally, On Day 1, I'd take a taxi to one of the closer beaches, taxi back to Cruz Bay for lunch, then have dinner on site; On Day 2, I'd book Island Roots charter (includes lunch); On Day 3, I'd schedule a hike with the National Park Service or enjoy a resort/spa day; On Day 4, I'd rent a car and drive to Waterlemon/Coral Bay.