Not inexpensive, but the hands on probable 'best' portable SW(SSB)/AM/FM is the Sangean-ATS-909X:
This teeny SW radio has probably the best signal to noise ratio of all portables .... meaning the 'faint' signals will be much clearer and with minimum 'noise'. Do consider the 'reel' type 'long wire' antenna for best SW/SSB reception ... and for boat reception get that 'wire' as high into the rigging as possible.
In the Bahamas and 'south' cruisers nets (local VHF) for weather are OK but are usually only a repeat of 'formal' predictions which are general, cover a very broad area and are easily misinterpreted.
'The' weather guru for these waters is Chris Parker at "Caribbean Weather". Here's a list of frequencies and times for Caribbean wx (Chris Parker), although this is a paid 'weather router' service, you can 'listen in':
Marine Weather Center - Marine Weather Center Services
If you will be including a 'laptop' during your travels, with the proper WeFax software, a simple computer to HF/SSB radio audio 'patch' cord, you can download via FAX the NOAA Ocean Prediction Center Charts for 24,48 & 96 hours.
Here's a sample of what you get: Ocean Prediction Center - Atlantic
The 'mother' of all WeFax websites (hardware and software discussions, recommendations, etc.) is WeFax.de
hope this helps