I suggest either one of the Carnival cruises - even though one of them starts in San Juan the ports of call are not that different.
IF you can get a cheap flight to San Juan I would take the Victory, but otherwise I would opt for the valor.
The Royal caribbean ships of that class are nice, but I think at your age you will have more fun on Carnival. I am assuming you like a little interaction with other people - dancing at night, etc.
I don't see many differences on your itinerary - so it is mostly a matter of the ship.
The two carnival ships are pretty similar - but I like the southern itinerary better - but not if you have to pay a lot more to get there.