This general route
is common and has been discussed here a few times so search for those threads.
Best time of year: typically April-May are most stable, being after cold front season and before hurricane
season. With the climate changing, who knows, but still the best bet.
Currents: Research Gulf Stream
, Gulf Loop, & Yucatan
Winds (& currents): See Pilot Charts
for historic trends.
Follow coast: No. Its a very long way, not very good cruising grounds, and lots of commercial
Suggestions/ Warnings: Respect the GOM...it can be a VERY ugly body of water
. Also consider using a pro routing service
like Chris Parker.