IMHO, get to the Gulf as soon as your schedule permits. Practice your basic skills along the way. By the time you get to FL, you'll have far exceeded whatever skills you'd learn on a Texas lake.
If you aspire to cruise the Bahamas, the longer you wait in the year, the longer you'll wait for weather windows.
As far as hurricanes go, once you get past the FL panhandle, western FL , unlike the Bahamas where I keep my boat, rarely faces any significant hurricane threat.
Good luck and fair winds!