You can have as many carry on bags embarking on the ship as you can Carry! Also, they must be able to fit through the luggage scanner which has a much smaller entry than at most airline terminals. We were on Mears transportation buses to Port Canaveral. All luggage that cannot fit under the bus seat in front of you or the narrow overhead bid, must be put underneath the bus with the luggage. That is the last time you will touch or see it too, until it is delievered to your room. I had no opportunity to retrieve my "carry-on" from the luggage compartment of the bus. Now if you are on your own by car or taxi, etc. then you will be able to take on what will fit. Signs say 11 x 17 inches at Port Canaveral.
I personally don't take any luggage that can't be easily carried, but that's just me. And all of it can fit through the x-ray machines. Most people many pieces of enormous luggage. When we got off our transfer from the airport, the porters asked us to identify each bag and check the cabin number for accuracy (I guess in case there were any last minute changes in cabin numbers which usually doesn't happen). We could have easily picked up our bags then and carried them on, but there was nothing in them that I really needed so we had them delivered to our cabin.
Most important is to make sure you have a swimsuit, sunscreen and sunglasses for the pool and some toiletries to clean up for dinner. You shouldn't need to dress up the 1st night. We didn't get our luggage until 8pm, some got theirs later but most got it much earlier. Most people ended up wearing shorts to dinner that night.