We haven't done a caribean in several years...make sure to find out what the ship caters to and make sure to look at the cost of extras (drinks, upgraded eating option, excursions, etc...)...When you see a dirt cheap cruise, it's really easy to burn thru more than the cost of the cruise on extras because they will be hammering them hard.
Also, the stops are usually just enough to get the tiniest taste of the destination. Plus many of the ports are overrun with cruisers. It's not unusual for ships to dump 5,000-10,000 people off for the day at a single port and most Caribbean ports are fairly small cities.
Also, most Caribbean cruises won't have anything remotely "exotic" about the food. Quality can vary quite a bit...higher quality (and cost) the older the crowd and the fewer the kids but also the less the night life.
More recently had the opportunity to do a couple European river cruises (work related...life's good). Drastically different experience. Higher up front cost but a lot less pressure to buy extras. Meals are all sit down and very high quality. Wine is included with dinner. Each port there is an included excursion (decent quality). You can burn thru some extra cash if you spend a lot of time at the bar and sign up for the upgraded excursions but again, not the pressure. The really nice thing is, with only around 150 passengers per ship, even if there are a few ships in port, it doesn't overrun the place...plus you are typically dropped off right in the heart of the city so you can usually just get off and walk if you don't want to take an excursion. (while they do stop in the dead of winter, they continue usually thru Christmas and start up again by March)