We took one two years ago January out of New Orleans to Jamaica, Grand Cayman, and Cozumel.
I booked an aft starboard balcony cabin with a LOT of railing space on Carnival. Of course the food was plentiful and I ate my share (and still lost weight during the cruise because I hit the gym daily).
Recommendations:
Book your shore excursions directly instead of through the cruise line
Drink the free juices instead of carbonated soft drinks due to expense
They will charge extra (at high rates) for anything beyond the agreed items. For instance, I asked our room porter to get us some water for an excursion we were taking and found it on our room bill at $6/bottle.
Find a message board for the particular cruise line/ship ports of call that you will be seeing to see what people are saying good/bad. I learned A LOT from those sites.
In Jamaica we played in the waterfalls and fed hummingbirds.
In Grand Cayman, we snorkled and held/petted/fed sting rays.
A bus ride from Cozumel, we toured Mayan ruins.
On board, we toured the ship's galley, took a line dancing lesson, took in a show, did some things you don't do, and generally relaxed.
Research the web sites to learn the different personalities of the cruise lines and the particular ships - some are no smoking - that would have been nice.
Look at the agencies that cater to interline discounts. I purposely booked away from when school kids would be out to have a saner trip but you may want that for family reasons.
Bon Voyage!