First, pick up a Non-Resident fishing license. As stated above the fines are pretty hefty.
If you're trolling, keep in mind that in that part of the gulf there isn't a lot of depth until you get a good distance offshore. Most shallow-running lures trolled from the back of a sailboat at speeds less than 4 knots will attract barracuda, but the best lure for these toothsome critters is a 12-inch length of bright yellow or bright red surgical hose tubing with a 4/0 treble hook at the back end. The front of the tubing is usually weighted with a 1/2-ounce bullet sinker. You'll also need a wire leader or you're lose lures as fast as they hit the water.
If there's no wind, and you want to catch something to eat, bottom fishing with live shrimp or squid strips will attract a host of great tasting fish. Grunt, yellowtail snapper, mutton snapper, and grouper are right at the top of the list. Be sure to check the seasons and size limits for these. Almost forgot, it's pretty risky to eat barracuda--they carry ciguatera, a neurotoxin that can be deadly.
Bucktails trimmed with chartreuse, 8-inch, bass assassins can lure cobia from the edges of deeper grass beds. Some can tip the scales at 45 to 60 pounds, but the average is closer to 20 pounds. Fresh cobia on the grill is outstanding, and smoked cobia is likely the best smoked fish I've ever tasted.
Once you reach deeper water there's always the chance of hooking up with blackfin tuna, most ranging 25 to 40 pounds. They hit like a freight train and they're not easy to land. They're pretty tasty on the grill, but personally, I would rather have yellowfin tuna. Trolling with topwater skipbaits lures the tuna, and they like their lures moving relatively fast 5 to 7 knots.
Large, shallow-running crankbaits and silver spoons trolled at 5 to 7 knots will frequently lure king mackerel, Spanish mackerel, and barracuda from the deeper waters of the gulf. The mackerel are fantastic tasting when fresh-cooked on the grill, but they do not lend themselves well to freezing.
The shallow grass beds are a great place to toss small bucktails trimmed with either a squid strip or piece of shrimp for speckled seatrout. Most of these fish vary in size from 12 to 20 inches, but there are larger ones lurking in the grass at times, particularly on cloudy days. This is another species that is best consumed while fresh--not frozen.
Hope this helps,