Assuming you are going with parents or someone at least 21, I suggest Carnival. You are not going to be able to buy alcoholic drinks on board, though. They are very strict about that. In the Caribbean countries, you can drink at 18, but do not miss the ship by drinking too much. The ship does not wait beyond the scheduled departure time for anyone – except maybe the Captain.

Personally, I would suggest you and your friend go to an all-inclusive resort in Dominican Republic. They have good beaches, good fun at the resorts, and no problem doing all the drinking you want. Everything is included at one price.