This is very subjective..and may take a bit of research as well.
Start by finding how many ships are in port on the day you will be there. The more ships, the faster things will fill up.
Study the ports and see what the consensus is as far as safety...for example many people feel safe in St. Thomas and take a taxi, many people don't feel safe in Jamaica and prefer to book with the ship.
If you opt to book with a private tour provider, find out their cancellation policy. The cruise line often lets you cancel if it's within 24 hours. If one of you is ill, sunburnt or just change your mind, can you cancel a prepaid cruise? Or what if your ship misses that port altogether.
As far as 'must do's' that is very personal for each cruiser.
One bit of advise....don't walk in with the 'once in a liftime' attitude and overspend like crazy. When your family sees how easy, relaxing, and affordable cruising is, you'll be hooked like the rest of us. You will be back especially if a particular port is really a positive experience for you.