Yes, you can save some $ by booking by yourself...Just remember when you do a ship excursion, if they are running late, the ship will wait, but if you go on your own, you ARE on your own, so keep that in mind and watch the time.
There is some good shopping in both St. Thomas and St. Maarten, but the bargains of years ago are just not there anymore. You'll see the same shops in both ports...If buying an expensive item, be sure to shop at home first, so you know prices...
As for food, hardly ever eat meals in port, enough is offered on the ship, but its possible there are some good places to eat. The ship does have decent burgers and pizza as well.
1. Is it cheaper/easier to book excursions to the beaches on our own or on the ship?
Get a taxi for your family, be sure to negotiate the price before you go and be sure it is a popular beach where you can get a taxi home again. In St Thomas for a beach I highly recommend Coral World. Spend the money to go in the park, spend an hour or two and then come out and enjoy the beach there.
For food, in St Thomas or St Martin, the main shopping streets should have some nice restaurants, but most people eat a big breakfast and then go out and wait for dinner to eat again.
2. Big shoppers in the family. Need to know any suggestions as to shops in Bermuda, San Juan, St Thomas, or St Martin
Shop in St Thomas (or St Martin), not San Juan. San Juan is great for sightseeing, go to the old fort & palace.
I honestly don't know Bermuda - its been too long.
3. For the foodies (Me). Where are the places to eat where we can get foods native to the island but also a good cheesburger or pizza.