Everything you would need, if you were staying at a resort hotel in the same geographic area of your cruise. Avoid over packing by reading the recommended dress section of the cruise literature that will be mailed to you after you book. Check to see if they have a theme night or talent show where you might need some special outfits. Even in the warm Caribbean, you might need a sweater on the decks at night. The air conditioning can also be icy. Pack some comfortable rubber soled shoes to get around on the decks. Bring a pocket calculator to help you figure your ports of call exchange rates. Bring a white T-shirt if you plan on going snorkeling or you may have a burned back when you are done. You might also pack some drinking straws to use while at port. This will help you to avoid touching your lips to a can's top. The top might be covered with contaminants that will make you sick.
Items of value that should never go in your checked luggage such as cash, jewelry, medication, travel documents and a list of everything in your checked baggage. Since luggage is often not delivered to your cabin until after your first dinner, be prepared and pack a change of clothes. You might also consider one-day items, in other words all the items you would need to make it through a 24-hour day, just in case your luggage goes missing. Keep lots of crisp one-dollar bills wherever you keep your money. This will come in handy when dealing with all the skycaps and porters.
If you are still at the airport, notify the Airline immediately. Hopefully, you'll have a list of everything in your checked baggage in your carry-on, so you can make them a copy for the claim. If the Cruise Line transferred your luggage and you never saw it at the airport, you'll need to work with the Cruise Line first.
Yes, find out from the Cruise Line how early you can board the ship and try to arrive early. You'll be able to avoid the crowds; you can use the extra time on board to confirm your seating assignment and be the first to make it to the sign up sheets. It could also help your budget when you take advantage of the free lunch that many ships serve while the passengers are boarding.
You may not get to see them if you fly in and they load them right on board, but if you have your own bags and are physically able, consider carrying them on yourself. If you booked a room deep in the ship and brought lots of bags this might be a task, but you'll have a head start on everyone else. You can be all unpacked and enjoying the ship while others are still waiting for their bags. It can take several hours for your bags to make it to your cabin and sometimes you get stuck wearing your dirty traveling clothes to dinner. Wouldn't a shower and fresh clothes make you feel better? There will also be less chance for your bags to disappear and some Cruise Lines state a liability maximum limit of $100.00 for your luggage.
You'll probably find your cabin steward who can show you how everything works. Make them your friend, they can be very helpful. If you have your luggage, it's nice to unpack so you'll get it over with and have some room in your cabin. You should check to see if your meal seating confirmations are in your cabin, if unacceptable, you need to go see the Maitre d'.
If you plan on using the spa, salon or babysitting service, find them and sign up before all the good times are gone. Check on the shore excursions if you know you are definitely going. See if you can sign up now, so you'll be sure to get on before they sell out.
You can book your cruise in calm waters aboard a larger modern ship with stabilizers. Book a mid-ship, lower level inside cabin, those have the most stable ride. Book a cabin with beds that are parallel to the length of the ship; the rocking is usually easier for your body to handle than a rolling motion. Speak with your doctor before you leave for recommendations of preventative medications you could use. Some people find an accupressure bracelet around the wrists to be helpful. Once on board, spend some time on deck and focus on a fixed point of the horizon. This helps your body to adjust to the motion.
Buy your shore excursions before they all run out!