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 for too.
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.
Sail responsively!
Cheers,
b.