The Sun is a great ship (we were onher in Dec 2004). Everyone has given you lots of good advice. My best advice is READ the Freestyle Daily religiously - lots of good, useful info like opening times of dining rooms and restaurants, activities, entertainment times and places.
Normally I arrange my own but since it is your first cruise you might be more comfortable booking with the ship. Personally for you I would recommend this for Belize and possibly for Roatan. Grand Cayman - it is pretty easy to arrange one yourself. On Cozumel - same thing or just go to a beach or go snorkeling at Dzul Ha.
Have a great cruise !