You will have a great time! The best advice I can give you is to relax and enjoy it from the very start. Many first time cruisers get uptight for the first day or two trying to figure out what to do next. Once you board the ship, read the daily newsletter that will be in your cabin to find out where to eat, what to do and so on.
Take a carry-on with enough stuff to get you through the first night (bathing suit, toiletries, change of clothes for dinner, etc.) That way, you won't have to worry about your luggage being delivered to your cabin and you can hit the sun right after you eat if you want.
Your luggage goes on with the porters, who deliver it to your cabin sometime that day - often not for several hours. If you want to change into a bathing suit to enjoy the pool or hot tub, it's a good idea to put those things (don't forget a coverup too) in your carryon.
You will also need a carryon for the last night of your cruise, to hold necessities (toiletries etc) and clothes for the next morning, as your checked bags have to be placed outside your cabin before you go to bed. Overnight the crew collects them and delivers them to customs after the ship docks.
Great question! Here is how to make the most of the first day.
Get to the cruise terminal early so you can be one of the first to board the ship. Get to your cabin and check your dining arrangements. There will be a table assignment either on your cruise card, or on a separate note in your stateroom. Visit the dining room and check out your table to make sure it is acceptable. If it isn't, go to the Maitre d' (who will be set up somewhere on the ship) and request what you want. Then hit the buffet for lunch (or the dining room, if you want) then either hit the pool area after changing into your bathing suit or go exploring the ship.
There will be a muster drill about 1/2 hour before you sail and you must attend. Wear you lifejacket, do the drill and then return to your cabin to drop off your lifejacket and start partying. There will be a sail-a-way party up on the pool deck, so jump in and start having fun.
Dinner will come and you will meet your table mates (if any) and the cruise is under way. Enjoy the dinner and the entertainment and whatever else you like to do. You can't miss.
Oh yes, don't worry about the menu in the restaurant. Ask the waiter what the dish is if you don't know and don't be afraid to send stuff back that you don't like.
You are right. On NCL - Freestyle dining requires no set dining time or table assignment. That will allow you the extra time to not worry about any dining arrangements and explore the ship. I always drop off my carry-on in my cabin (as Tom and Karen suggested - always packed with the things that will get me through the first day/evening without worrying about luggage) and start my exploration of the ship on the upperdeck. Luncheon is usually served at the casual dining buffet. After sampling my first meal onboard. I acguaint myself with the ship - moving from top to bottom. After I have finished my tour, I head for the jacuzzi or pool for some relaxation before the the muster drill. If this is your first cruise, make sure you take in the first night's show. You will be introduced to many of the staff and get a sampling of what is in store for the rest of the cruise. ENJOY!!!