For a variety of reasons, I am going to make a STRONG suggestion that if you intend to pursue cave training in florida, you purchase DSS gear.
As for regs, hard to go wrong with ScubaPro. Apeks are also popular, but many are not purchasing AquaLung products any more for political reasons. Your call. You will not find much OMS down here.
You have gotten some recommendations on instructors. I too am looking at cave instructors and have some strong feelings. My first class will be with Jeff Bauer. I will be taking cavern with him. Some have suggest Rick Murcar for cave. I've met Rick and consider him to be a stand-up guy and have heard great things about his teaching. You might also consider Larry Green who has been voted NACD instructor of the year two years running (you better have your stuff together before you take his class though). You might consider David Rhea. Jim Wyatt is also an excellent instructor from what I have heard. Heather Choat is also a very good instructor from what I hear from my friends, and she is very active in the dive community. There are undoubtedly others who are also good.
One of the things you will have to do is to pick one of the agencies with which to get your training. The most popular seem to be NACD, NSSCDS, and GUE. I am not sure if TDI do cave training or not, though I know Larry Green is affiliated with TDI. Be forewarned. There is a LOT of political baggage between the organizations so you'll be dealing with that to a degree. I suggest you try to find the best instructor you can afford, prepare well for class, show up and work hard. Discuss gear choices with them. They will assist you.
One last thing. Though this may be somewhat controversial, I would suggest you NOT try to do cavern through full cave in one shot. I'm not saying it can't be done, but there is SO much going on in the training, from my perspective it seems best to get some real diving experience between each of the levels and let the training sink in a bit before going on. I intend to get 50-100 dives between the levels if possible. Of course I have easy access to the caves so that is tempering my decision.
Regardless, best of luck to you in doing this. And dive safe.