I can't really add too much to what has already been suggested for the dives themselves. AWAP, Jim, Txyaloo, RH, RonFrank and GOG are spot on. The only things I might add are generalities that apply to most open water experiences.
Be fit. The FG can be docile---I've seen it plate-glass flat out there---but it can also be running 3-5 feet. That means the Fling, being moored, will "saw" considerably in the swells, and THAT means the big ladders will be punching holes in the water. Getting aboard under those conditions requires some finesse and patience, but it also involves at least a little strength. Be ready to grab and climb, and that means with all your gear (except your cameras...they drop a line for those).
Be dressed for the occassion. In the summer, the water will be in the 80's pretty much to depth. While you don't need a lot of exposure protection, I still like to have most of my skin covered (I don't wear a hood, of course) to protect against the "no-see-um" stingers. It's not a significant problem, but they can be annoying. Also, wear gloves. Most folks maneuver down and up the mooring lines, and lots of sharp critters attach themselves to the lines, so protect your hands.
Be attentive. As someone noted in the other forum..."the Gulf ain't no swimming pool". From watching for people under you as you splash, to monitoring your partner, to always knowing where you are in relation to where the buckle is, BE AWARE. Maintain your situational awareness and remember that conditions can change in a heartbeat. That's the reason I say that a diver should know where the buckle is and not the boat. I've seen the Fling swing a full 180 degrees on the mooring line in less than two minutes, and that means it changed its position by a hundred meters or so (the folks still on the boat said it was really freaky for them, too). That buckle isn't going to change locations, so all navigation usually uses that point as the main reference.
As for remembering where you are, recall that you are 110 miles out. IF something should happen...injury, DCS, ANYTHING...it's a loooong ways to a fully staffed medical facility. While it's possible the Coast Guard can make it out there, they might not be able to, and that makes for a long trip home when you're needing medical attention. Not only that, but it's no way to make friends with the others on the boat...you just ended their diving trip. Be considerate by staying safe.
In that same vein, READ the FAQ provided by the Fling Charters website. It answers a lot of questions about how the boat is run, the rules, and what is expected of every diver.
And I can only reiterate what has already been said...LISTEN TO THE BRIEFINGS. Those folks have been out there hundreds of times and represent thousands of hours of experience in the Gulf. Use that wisdom as your guide. If you have questions, ASK. Then follow their advice. If something doesn't feel right, then sit it out. The Gulf will be there another dive or another day or even another trip. The diving is spectacular, but it's not worth putting yourself at risk. (Okay, forgive me, but I have to tell one story. The first dive of the second day saw the currents just RIPPING. Our group--science teachers, marine biologists, and NMS personnel--circled up for the briefing. They explained the conditions and said, 'We're not saying you can't dive, but those are the conditions and you have to decide if you can handle it." It got quiet for about 20 seconds while we thought it over. I was one of the "more seasoned"--read that "OLDER", not more experienced--of the group and I became aware that they were waiting to see what I was going to do. I looked around and finally said, "Ya' know...I don't have anything to prove. I think I'll go see what's for breakfast!" Three divers decided to brave the current and they did just fine...except that they said the current kept blowing their masks sideways while they were on their rest stops! Yup, the current can be pretty brisk out there.)
This one doesn't relate to safety, but enjoyment. Read up on what the FGBNMS actually is and spend a little time learning what you might see out there. There is plenty of info at the FGBNMS website, and other sources such as REEF will help you with identification of species and such. Knowing what to look for can make a trip far more fun and will help you relate your experience to others when you return.
That's all I got...sorry it's so wordy, but as you can probably tell...I like the place. Have fun out there!