Antigua is on some, but not all, southern Caribbean itineraries. We were recently there on Golden Princess, and shared our port day there with Norwegian Spirit and Celebrity Constellation. Other ships go there too, on different weeks. I posted a brief cruise review on www.cruisereviews.com,
which you can check if you like.
If you are new to cruising, or just want to have access to all kinds of options, I'd recommend you work with a cruise-oriented travel agent, who can help you choose the cruise line and itinerary that you will most enjoy.