I would recommend either Carnival or Royal Carribean. Both lines tend to attract a younger crowd. We've been on both lines and found a lot of people on board in their 30's-50's. Haven't cruised Princess yet but someone else might be able to give you more info on that line. I've also found it tends to be a younger crowd on the 4-5 day cruises. Hope this helps.
so much depends upon what you are looking for. If you are looking for a lively, party cruise with great shows and nightlife then i would look into Carnival or RCCL.
If you are looking for a casual-elegant cruise that still has lots of activites and nightlife then look into Princess
If you want something laid-back, a bit more elegant and more of a "traditional" cruise experience then look into Celebrity or Holland America.
If you are looking for beautiful beaches and great shopping then pick an Eastern route.
If you want something a bit more active, more adventure then pick a Western route (swim with Sting Rays, climb waterfalls, snorkel, dolphin swims etc)
If you are looking to experience more of the local culture/history and flavor of the Caribbean then pick a Southern route.
I would recommend sitting down with a travel agent - one who has lots of cruise experience and just pick his/her brain.