Hi Roweboat,
Welcome. Hope you enjoy ScubaBoard... it has a wealth of information and lots of experienced divers who can help on most anything. I find it a great way to waste my lunch hour!
First things first... there are several certification agencies out there and they are not all the same. If you don't know who they are... just use google! Going with the certification agency affiliated with the dive shop that is geographically closest may seem to make sense now, but you could have second thoughts later. Talk to other divers and get their opinion. Also while you are new at a sport it is hard to imagine where your interest will eventually take you... so at least in a general way look at what the different certification agencies offer for training beyond just the open water level. Please trust me on this one... as I learned the hard way from my own personal experience... not all instructors are the same. Some are good, some are great, some are to be avoided at all cost. Check out the dive shop and your instructor before you sign up for classes!
Advice as to what to buy first? Well you can buy new, buy used, or rent. Maybe even borrow here and there. Take your time... don't hurry. Look at what other divers use, ask for their recommendations and experience with various brands and models. My first purchase would definitely be a mask. Make sure you get help to ensure it fits properly. Followed by fins and a snorkel. Most instructors expect you to provide these during your open water course, though there are exceptions. My second purchase would be exposure protection and there are lots of choices that you should discuss with your local dive shop based upon the water temperatures of where you expect to be diving. I'd wait a bit on everything else since there really is no hurry and plenty of rental options available on nearly everything. Some scuba gear is a major purchase and no sense in rushing into something you might regret later!
I'd also hold off on the thought of diving in a local river until after you have logged a bunch of dives and have some practical experience in various conditions under your belt. You could possibly be dealing with cold water, swiftly moving water, low vis, shallow water/boat traffic, underwater obstructions, or a combination thereof. More than likely the river will not be quite as pleasant as your Caribbean experience.
Best of luck with your training!
