DP has been an avid cruise do'er, he has done 22 cruises, 14 of these round the Caribbean.
He has been on P&O and TUI, both are great.
Cruise and stay is a good first choice of cruise, because if you don't get on with the cruising, you know you have a week on land at the end.
However, he says he guarantee you will book two weeks on the ship next year.
£5000 is more than enough for a fab holiday and for this money you may be able to get a balcony cabin.
Best time - Anytime between Oct and April
Islands do vary, each has it's own personality. So any combination would be a good one.
Go with Tui if you want cruise and stay
And P&O for the full cruise experience.
If you get sea sick, you can have an injection, about £70, which will sort the problem.