my mom and i want to go on a cruise but we arent like rich so we would need a cheap one we want to go on one for my 13th birthday so i like want kid like things on the cruise my mom wants like carribean music and whats the best cruise line ????
To give you the opposite answer: Holland America Lines is known to be a bit more conservative (quieter, and appeals to the older, more sedate cruisers; with more business casual to formal dining in the main dining room) than the other lines {so less young teen activities}. [ idk specifically about their Caribbean cruises, but am guessing it is similar. ]
But then again, a cruise is about family time (uninterrupted by computer, TV, cell phones, etc) and the ports of call and the tours and adventures available at each port if you want them. {or just walk around and see the sights, and maybe have a small meal of the local food if you are hungry.} - so do not automatically rule out HAL.
Given your age, and doubting your mom wants a "party" boat; as I read it on here, Disney is a good choice (but cost may be a little higher - since they do not sell as much alcohol; and have no casino income). Search the internet, then ask a travel agent when you have a better idea of what you want.
Cruising can be quite enjoyable and fun. So Happy Birthday!