The caribbean is the best and crusing can be great if you ask the right questions. What is you travel style ? If you like the structure of knowing when dinner is served, like to paticipate in groups and just want to sample the caribbean, then I would suggest a cruise. However, if you style is more like mine, in that the only decision I want to make in the carrinbean is what cocktail to have for breakfast and my whole day is spent finding out where the locals eat then I would not suggest a cruise. All cruise ships have one thing in common, service. The joke is when you get up in the middle of the night to visit the restroom, your bed is made again before you return. That is the truth. The food - too much and it is all great.What islands - if you go western, then you will hit Mexico and that is not a bad thing, but not so much the caribbean style that you might be in search of. Anyship travelingin the the lesser antilles -St. Kitts, St Martin, St. Lucia tends to be smaller and the ports of call still are working ports as well as shopping meca's. Think about what is important to youand then find it - its is out there.
The best Caribbean cruising is in the Eastern or Southern Caribbean. They are more beautiful and less busy/commercial stops. Be sure to include a stop at St Maarten or St. Thomas for the best duty free shopping but otherwise try to get to some of the smaller islands.
If you really want to splurge, pick one of the Windstar cruises. They are small motorized sailboats, and therefore are more able to get into smaller ports, like Pusser's at Virgin Gorda, BVI., etc. Also, the staff is super friendly and the food is fabulous. Another fun cruise would be to pick one of the Windjammer Cruises. You will find lots of activity on those and make fast friends, those cruises are great fun if you are young, or at least "young at heart". Good Luck!
We prefer the smaller boats, and I agree that Windstar is good choice. For something really special you might also look into SeaDream. These are 100-passenger yacht-type ships. The service and food are extraordinary. They also visit the smaller ports, such as BVI. The Star Clippers are also a lot of fun. These offer more of a real sailing experience than Windstar, where the sails are more for show (although beautiful). The Royal Clipper has an excellent itinerary to the Grenadines from Barbados. Hope that gets you started!
We did the Eastern Caribbean cruise with Royal Caribbean and it was excellent. The ship we were on was Navigator of The Seas and it was HUGE! If you are looking to try a small ship then this would not be for you, but if you don't mind the larger ships thenI would recommend it. We sailed from miami and stopped off at the Bahamas,San juan,St. martin and Labadee(amongst others)which is their own private island and very nice! There is so much do to on these ships, including an ice skating rink and rock climbing wall. The evening entertainment is first class too. Good luck on choosing a cruise ship.I am sure you will have a wonderful time whether you choose one of the larger or one of the smaller cruise ships.