We just got off the Fantasy yesterday. We did the Baths on our own, and it's very easy to do. You get off the ship, and take about a 10 minute walk to another dock and catch the Speedy's ferry. You can pay onboard for the taxi ride to and from the Baths, and they give you a wristband. The fare for the roundtrip ferry and roundtrip taxi to the Baths was $38 for adults and $28 for kids. I don't know if they take credit cards. Everyone we saw paid in cash. There is a small admission fee to the Baths - I think it was $3 for adults and maybe $2 for kids?
Speedy's leaves the dock at 7:45. You can make it if you get off the ship as soon as you can disembark (we never heard an announcement that we could begin disembarking, so don't wait for that or you won't make the first ferry). Speedy's makes a few trips a day, but we wanted to get there early before it got too busy.
We have been to both St. Thomas and St. John and prefer St. John - however, it really depends on what your group is interested in doing. Last week, we did the "St. John On Your Own" excursion through Disney. The boat ride to and from on the Island Princess was great because a crew member talked the entire time about the history of the island, pointed out interesting landmarks and celebrity homes, and shared fun facts. I doubt you would get that on the public ferry.
In St. John, you have to take a taxi to get to Trunk Bay but there is a neat shopping area right by where the boat docks in Cruz Bay. We snorkeled for an hour in Trunk Bay which was really cool - there is a coral reef there with lots of colorful fish.
All of those islands have large open air taxis so it won't be a problem for all 9 in your party to ride together.