HI Big Red, I'm a big guy too. 6'1" 300lbs. It's often difficult to find gear that fits us larger people. For instance the the bigger names in wetsuit's have a size chart and the chest size doesn't even go beyond 48. Even in the biggest size they have! One day, I will get a custom suit, but for now I was able to make a 4XL Akona work for me, and you might too. Still a little tight across the chest but at $100, I'll live with it.
The fitness thing can be a big deal if your cardio isn't up. The class requires that you do a 200yd swim and a 10 minute tread water. Not too difficult for larger people, because we tend to float. So it's not a good gauge of fitness for me, don't know about you. Anyway, according to the physiology section of the class, being over weight increases your chances of getting bent, and if you aren't fit, you will be working harder, and breathing heavier, which increases those chances even more. So make sure and pay attention to the fitness aspect. I work out for 45 minutes in the morning 5 days a week to keep my cardio up.
The BC is probably going to be a problem. The 2X BC that I used for my intial class, and rental gear over the last year don't fit right at all. I never found one that did. Just like the wetsuits, they aren't made for bigger people. It's like they just upsized the smaller stuff because they had no one to work off of. When I finally bought gear, I bought a back plate and wing, which, if you hang out in these forums for any length of time, you'll read plenty about. You should probably just see if some shop has a jacket BC that will get you by first though. Then you can make an informed decision about it later. Once you find a BC that will work, then call to where you are going and see if they have one that will "do" for rent.
I hate wetsuits. If you're like me, you have plenty of room between your core and your skin and can comfortably dive in waters down to around 70 degrees for extended periods without getting cold. However, without exposure protection, you open yourself up to all kinds of fun stuff. Last year I was diving with no wetsuit in the keys, ended up getting jellyfish polyps stuck in my back. VERY irritating, and it lasts for a couple of weeks. From then on, no matter what the temp of the water, I wear the wetsuit.
Fins... Don't let the dive shop talk you into split fins. They will say it reduces effort, and they're right, it does. But your legs are used to carrying around all of that weight, so when your in the water and weightless, you can handle a good solid fin. XL Scuba pro jets are good except that the pocket isn't tall enough and will crease the top of your foot. Good fins though. Avanti Quattro by Mares in the XL size is a good fitting fin for a bigger foot. Even with a hard soled dive booty on. That's what I use unless I'm diving in current, then the jets come out to play.
For weights, again, the dive shop will likely have no idea what it takes to get you down. They will likely continue to insist that you only need 12 or 14 pounds. I need 30lbs of lead to get down in saltwater with a full 3mm suit on. You may need more. Weight belts aren't comfortable with this much weight on them. You'll have to offset some into integrated weight pockets on a BC, and probably find a couple of other innovative ways to hide weight on yourself

That's one thing that led me to the back plate and wing, but like I said, that will probably come later for you.
Anyway, good luck, and definitely take the classes local, then do the dives as a referal in the tropical waters. You won't be sorry.
Jason