Celebrity would be just fine for any time, although I still haven't tried them out, but hear nothing but good things about the line. Any idea where in the Caribbean you'd like to cruise? Western is a little more for the water sports, less good shopping. I personally love the Southern, plenty of different islands, good shopping and beautiful islands. Its really a matter of choice as to what you and your husband like to do.
Once you narrow your search down, you may want to use the bargain finder here to get specific prices for a ship, time, etc that you want to do. This is a great tool and many have found exactly what they are looking for when finally deciding on a cruise. Good luck and I'm sure you will love cruising. Let me know what ship and line you finally decide?