MANFOD
To quote you:
'I suppose Miami with connections to S America and the Caribbean, plus potential cruise business, is the obvious candidate.'
AA/Miami is often assumed to be the best way to connect to the Caribbean and South America, but it isn't.
Delta's growing network out of Atlanta to this region places it streets ahead right now by all the measures that matter to me:
AA vs Delta = Delta just have a much better TATL product. Service seems to matter. AA frankly offers a pretty naff, indifferent product and service.
Miami Airport vs Atlanta Airport = Atlanta is a very well run, pleasant and efficient airport / Miami Airport at times feels like the gateway to hell.
The overall transfer experience = Delta/Atlanta wins hands down. On many transfers you get to check your bag thru to final destination unlike Miami. Border and security at ATL are both well staffed, courteous and efficient - all the things they aren't at Miami.
Given we already have Delta to Atlanta (Business Class of 36 and pretty rammed when I'm on it) we're pretty well served I would say.