As Robin said - welcome to the cruise board. As for basics - well I think most everyone here would agree that
DCL is the way to go. You have a number of choices:
3 or 4 day cruises which go to the Bahamas. The 3 day leaves on Thursday gets back Sunday and you go to Nassau and
Castaway Cay (Disney's private island). The 4 day leaves on Sunday and gets back on Thursday and you go to Nassau, Castaway Cay and either have a day in Freeport or a day at Sea (it alternates). Both of these are on the Disney Wonder.
7 day cruises on the Disney Magic sail Saturday to Saturday and alternate between an Eastern Caribbean (St. Martin, St. Thomas, Castaway Cay and 3 days at Sea) and a Western (Key West, Grand Cayman, Cozumel, Castaway Cay and 2 days at Sea)..
Carnival sails out of Port Canaveral as well with pretty much the same options and ports (except Castaway Cay of course).
Holland America sails the Zaandam on 7 day Eastern and Western cruises in Winter only.
Royal Caribbean sails the Sovereign of the Seas on 3-4 day cruises and coming in November of 203 will be doing 7 day cruises on the Mariner of the Seas (Eastern & Western Caribbean).
There is also a small ship called the Mirage that offers 2 and 3 day cruises to the Bahamas and Key West.
Hope this helps!