You didn't mention where you are from, so its hard to say what the best cruises for a "budget" would be. We live in Texas, so leaving from Galveston means you don't have to pay for airfare. Same can be said if you live close to New Orleans or any of the other cruise ports.
Assuming that you choose your port wisely, then which cruise you gone on may be limited. Cruises from Miami can go anywhere in the Carribean. St. Thomas is nice, St Martin also. Avoid Freeport and the Bahamas if you can because there really isn't that much to see. We like the western Carribean port (Grand Cayman, Cozumel etc.. (Note that I didn't include Jamaica in that list. Jamaica would be nice if everyone you came within a hundred yards of didn't demand a handout or for you to buy some piece of junk)
Most cruises you can go on would be nice for an anniversary. You really can't go wrong. They are really what you make of them. Go and have fun!
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013