The best thing to do is to get some cruise brochures. Probably your best bets will be with Carnival, Royal Caribbean (RCI) or Norwegian Cruise Lines (NCL). Some others may have further suggestions or different views on this.
If you have never taken a Caribbean cruise, your best bets are either Eastern or Western Caribbean. Southern Caribbean cruises normally go from San Juan, and I have found the airfare to be more expensive than going to Miami or Fort Lauderdale, etc.
Next, pick the time you want to go on your trip and see what ships are sailing where. List all the ships that are sailing during that timeframe for these 3 cruise lines. Then, look over the itineraries for each one. Do you have a particular port in mind that you wish to visit?
Next, go to www.mytravel.com
and look at the different pics of the ships that you want to go on. What kinds of things do you want to do on board? You'll be able to look at the different amenities on the different ships and narrow your choices.
After you've done all of this, next, read reviews of all the ships that you've selected and list the pros and cons of each one. Price, as well, may be a factor in choosing your cruise, based on your circumstances.
Then, try to narrow down the choices to a few. Call your travel agent or the cruise line directly to get some pricing on inside cabins (no windows) or outside cabins (with windows). Sometimes, they have "deals" through the cruise line.
Anyway, good luck with your choices and have a fun cruise!