What are some money saving tips for a carnival/royal caribbean cruise? What is the cheapest price for a family of four for 7 days?

My family consists of my parents who are 57 and 51, my brother who will be 21 at the time and myself at 18 years old. I’m planning our vacation for this summer and we’re taking a Royal Caribbean cruise somewhere in the Caribbean–probably the western islands. It’s our first cruise but we have no idea which ship is a good choice since there are so many of them..any suggestions?
or even a different cruise line if you think a different one would be better for my family.