Out of your ports, St. Thomas will be the best for shopping. Antigua has 365 beaches. My recommendation there is to negotiate with a driver outside of the terminal to go on a tour. We did one for $25/pp. He took us to Shirley Heights, Nelson's Dockyard and a nice beach with a restaurant/bar. Barbados, if you like snorkeling, do the Tiami catamaran sail/snorkel through the ship. The Tiami crew are wonderful, their catamarans are immaculate, and the one with the lunch has wonderful food. They usually great you with a mimosa for the early sail/snorkel. St. Kitts is a beautiful island, the batik factory is a good stop. My suggestion there is to do a tour through the ship, a "best of" or "island" tour. St. Lucia is one of my favorite islands, a snorkel to the Pitons is wonderful. We also did Pigeon Island, if you want to do that, I'd suggest taking the ship's Pirate tour. We paid the driver $85 each way to get to Pigeon and then had to pay an entrance fee. The Pirate ship was $49/pp. They didn't get to stay as long, they stayed about 1 1/2 hours, but it was a LOT less expensive.
Hope this helps some.