I have taken two of each, the 3, 4 and 7 night cruises and of course the longer is the better.
That being said, the 3 night will give you the BEST of the BEST. You see all three of the Disney themed shows, dine at each restaurant, and visit
Castaway Cay and enjoy the pirate night deck party. Those are the main highlights of the cruise, and you will get to do each of these.
If you want to try Palo, you can 'double dip' and go to the main dining first and then go to Palo later for a second dinner. We have only been to Palo once and we are fine with just using the regular dining, but we like having dinner with our kids and Palo is adult only, so we just skip it.
As for tips for making the most of your 3 night:
1. Stay on the ship when you dock in Nassau. Use it like a day at sea and just enjoy the ship.
2. If you have kids, make sure you take their swimsuits with them at the time you board so they can swim right after you have lunch (we actually just go straight to the pool and my kids are usually the first ones in, and we just have pizza and burgers for lunch, but since this is your first one I suggest you go to the buffet).
3. At Castaway Cay make sure you get off when they dock and enjoy the whole day there! It is wonderful! Our favorite activity (beside just hanging out at the beach) is taking the bike trail, but do it first thing before it is really hot.
4. Don't miss any of the shows. They are great!
5. Try to order room service once at least (the kids think that is so cool and there is no extra charge for the food, milk, coffee or tea--soda is free on deck 9, but not with room service).
You can have a great time on the 3 night, but you probably won't relax too much. That is the main thing that is missing from the 3 night (relaxing). But you can experience all of the fun!