It's kind of hard to give you an idea without any idea of what you are looking for. For example, what ages will be going, budget, length, etc. But here is a general answer for you:
If price doesn't matter, I would say either Oceania or Crystal and Celebrity, which I believe has been rated the best line. All are fabulous cruises and they are wonderful. Here would be my order of preferance:
1). Crystal
2). Oceania
3). Princess
4). Disney
5). Holland America
6). Royal Caribbean
7). Norweigan
8). Carnival
Celebrity is also pretty good, I would throw that somewhere in the middle. Oceania and Crystal are great and the best if you are wanting a bigger cruise line and not if you wanting a more intimate, small cruise. Windjammer is one example of a small cruise line, but there are several out there that are really good.
Royal Caribbean, depending on which boat you use, is one of the most popular lines. There prices are quite low compared to others, but the quality is very good. Disney is a little more expensive, but one of the nicest you can take. Carnival is a low cost cruise, but is known as the Las Vegas of cruise ships, there is lots of parties, smoking, drinking, etc. Celebrity and Oceania are more upscale and luxury lines, but are also more costly. Carnival and Royal Caribbean tend to have younger crowds, with Carnival being college aged kids. Royal Caribbean and Disney tend to have more familes. Princess, Holland, etc. tend to be older crowds.
Assuming you are younger and want to have a good time, I think Royal Caribbean would be a good choice. The overall quality is better than Carnival, it is a little more classy, but you still get good rates.
Really, all the islands are great, so go with the one that fits in your budget best, the one that is on the boat you like, etc. The best thing is to just look over the different options and what the lines offer that you like the most, because they are all good.
Here are some links that should help: http://cruisecritic.com/ports/area.cfm?area=8
http://cruisecritic.com/ports/area.cfm?area=10
http://cruisecritic.com/ports/area.cfm?area=9
One final thing, if you are planning to book a cruise, I would contact a travel agent hat specializes in cruises. Trust me, it is a lot smarter way to book than using online discounters, I've read way too many stories of people that have had their trips ruined from using sites like these. Most of the time my agents prices are lower than these discounters, sometimes they are the same and very rarely they are slightly higher. But the service and knowledge you will get is definitely worth the extra cost.
Hope this helps!