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 currents
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 traffic/rigs.
Suggestions/ Warnings: Respect the GOM...it can be a VERY ugly body of
water. Also consider using a pro routing
service like Chris Parker.