What are your ports of call? Since it's the Western Caribbean, I'm assuming they're Grand Cayman, and Cozumel?
Seeing as how this is your first cruise, I would book with a travel agent, and not through Carnival when it comes to booking your cruise, if you haven't done that already. As far as excursions, I would book through Carnival, since this is your first cruise, and you are not familiar with the ports. If Jamaica is in your plans, then I definitely would book through the ship, and not on your own. Cozumel is safe to do on your own, but it depends on what you want to do. Both times I went there, I just took a cab to a beach club, and had a beach day. Carnival is a great choice for your age group, and I think you may find lots of young adults on the cruise.
As far as weather, safety is the #1 priority of all the cruise lines. Should hurricanes interfere with a port, they will either revise the ports of call so they can miss the hurricane, or if they have to, skip the port all together. This happened to me last time. The weather was bad in Grand Cayman, and it was deemed too dangerous for the tenders to run passengers ashore, so they cancelled the port. If this happens, any excursions you booked through the ship will get refunded by means of an onboard credit. Any excursions that you booked independently, get in touch with the tour operator to see what their refund policy is because of bad weather.
I know I mentioned tenders before. This is because in Grand Cayman, the water is too shallow near the shore for ships to dock, so they must anchor out in the harbor, and use tenders, or small ferry boats to ferry passengers to shore.
2007 - Majesty of the Seas
2009 - Enchantment of the Seas
2010 - Freedom of the Seas