The Caribbean is where most people's first cruise happens, and it's also where the biggest gap opens between a week you'd repeat and one you wouldn't — almost entirely down to which ship you're on, not which islands are on the itinerary. Eastern, Western and Southern routings all hit a similar rotation of beach days and port towns; the ship is what you're actually paying for.
Celebrity Edge — Eastern Caribbean, round-trip Fort Lauderdale (7 nights) — The ship we'd actually put a first-timer on. The Edge Villas and the Magic Carpet platform are the two things photos never quite capture, and the food is a real step up from the mass-market standard without the price jump of a luxury line.
Silversea — Southern Caribbean, round-trip Bridgetown (10 nights) — Same small-ship logic as our Mediterranean pick below — all-suite, all-inclusive, and it gets into harbours the big lines simply can't dock at. The Southern Caribbean islands it reaches (Grenada, the Grenadines, Tobago) are the ones a mega-ship itinerary skips entirely.
December through April for reliable weather and lower humidity. June to November is hurricane season — itineraries can be rerouted with little notice.
Fort Lauderdale, Miami and Port Canaveral cover most Eastern and Western routings.