My husband, 2 kids (7 & 5) and I went our first cruise this past week. Also, this was our first time out of the country. We sailed to Half Moon Cay, St. Thomas, San Juan, and Grand Turks.
Let me start by saying, I have no other experience to compare to. My husband and I finally (after 7 yrs) got to spend some time doing things we wanted to do. From the start I felt comfortable with my kids going to their camp. They were occupied and we were still close by. The kids made many friends and the staff was amazing with them.
I planned out the whole trip before we left and wound up changing a lot once I was on the ship. I planned for our kids to go to every port with us. The kids weren't interested at all until we hit Grand Turks. We took them to the beach which they loved. Carnival was very gracious when I had to return my kids tickets for some of our excursions. My husband and I got to enjoy them ourselves while our kids were at camp.
We stayed in a Balcony room. The kids got to sleep on bunk beds (which my son is now begging me to buy one for the house, lol) We had enough room to put our clothes away and stored our luggage under the beds. Every morning our room was cleaned and every night the staff turned down the beds. My kids always looked forward to seeing what towel animal the staff would make.