Unfortunately, this depends on where you are in the Caribbean. This is to say e.g. rum from Trinidad may be hard to get in Martinique
and rum from Dominicana or Cuba
can be easily bought in Auckland
I would take Trinidad and Martinique
rums - hard to get abroad, great choice, great palette and a head
above what we normally buy ion stores and consider a 'Caribbean rum'.
Another factor is which rum you like best. Some like white 'country' rum, others like white distilled, others may prefer gold or brown aged rum. Some Caribbean rum liqueurs are absolutely worth diving
If I were to sail away with my hold full, I would definitely take rum from Martinique and from Trinidad.
Mind you are supposed to report and possibly lock this hold in Panama and in every consecutive country. Be super careful in French Polynesia
as they get totally pissed off and CAN impound your boat for any major amount of unreported liquors there.