I agree with everyone about the 7 day cruise being the perfect first cruise length. Your first and last days are spent getting settled and then getting off the boat leaving you with 5 days to do excursions and explore the boat.
Other tips are:
1. The food is usually awesome so bring clothes that will accommodate the possibility of feeling bloated at the end. A cruise is not the time to be on a diet!
2. If you like adult beverages get the drink package. Chances are you'll spend more on drinks anyway as they get pretty pricey. If you're not sure and then wish you had bought the drink package keep in mind they usually run a half price promotion half way through the cruise (at least this have been our experience on other cruise lines).
3. Spend the money and buy at least one drink out of a hulled pineapple or coconut. Take a picture! Trust me, this is a fun keepsake.
4. Bring some zip lock gallon baggies and a small box of powdered laundry detergent. This way you can wash your swim suits (plus under garments!) in the small sink in your room without spending the arm and a leg they'll charge you for laundry service. The rest of your clothes can usually be re-organize if needed but the Carribean sun is no joke and you're going to want to clean the things you sweat the most in.
5. Excursions get expensive but I always recommend splurging on at least one. You may never have an opportunity to swim with dolphins in in turquoise waters or zipline thru a jungle canopy again. Our last cruise we splurged on a zipline and river rafting trip and it was some of the best memories we've ever made. We had so much fun and I don't regret spending the extra $ on the one we really wanted.
I could talk cruising all day but these are the big ones that I can think of off the top of my head.