Frank,
I see this thread is a few days old, sorry about the late response.
I am a long-time skier and an occasional snowboarder and I used to teach both disciplines, so I will offer what advice I can.
Before buying a board, binding, boots you should(as was mentioned) either rent or demo different types. Just like skis, certain boards are for certain types of riding.
So, ask yourself what type of riding you will be doing, more than likely you will end up with a dual-tip board(as opposssed to a straight speed board), a dual tip(the lingo may have changed since my teaching days) will allow the board to work in either direction. I prefer a board with some flex to it, when you are staring out, a softer board is easier to carve with--save the stiff boards for later--although this is also up to personal preference. Length--as a rule of thumb, we would typically try to have new riders set up with a board that at a minmum came up to thier chin, and at maximum came up to the forehead. Longer boards=more speed, but are harder to learn on. when trying out boards--stand on it(with the snowboard boots on) in the approximate postion you will be riding--this is critical since you don't want a too-narrow board that leaves your toes or heels poking beyond the board--they will hang up when turning. That should help you with board--twin, tip, medium-soft, wide enough for your feet, and no taller than your forehead--brand of board is up to your budget.
Boots/bindings are a personal choice, I have seen people board in regular Sorrels--although snowboard-specific is the way to go.
Just find a pair that are comfortable--as with skiing, boot fit/comfort is the most important aspect. Some boots have internal alcing systems, some are conventional. However, depending on the type on binding you get--may determine the type of boot. There are alot of options for "step-in" snowboard bindings. These are very convenient--you don't sit in the snow while strapping in/out, you just step in/or release. But these bindings are a little more $$$, and you buy the boot with them, since they have the appropriate attachment hardware that makes them work as a sytem. Personally, I don't care for the step-ins as I didn't think they gave me the "feel" of support that I like when boarding that I get with the traditional strap bindings. Plus, strap bindings are cheaper, and (I think) more adjustable--the downside is weta$$ from strapping in/out, but when learning, you will be on your a$$ alot.
Don't bother having a shop install the bindings--unlike ski bindings, anybody can do it--you just screw them into the position that is most comfortable--the board will be pre-punched for various configurations.--You don't want the bindings mounted so your feet are any wider than shoulder width apart, and you want your knees slightly bent--then fine-tune your stance--will you ride goofy or regular? Which angle feels most comfortable for your feet--you can rotate bindings for virtually any postion, I have seen both feet angled downhill, to total duckfoot stances. What works for me is rear foot straight--or slightly tweaked back and front foot at about a 45-degree downhill angle. Don't forget to get a stomp pad and leash(some shops will "throw these in" if you are buying a complete set-up. Let me know if you want any pointers for starting out--I will post back a typical beginner's 45 min. lesson--all the basics to have you comfortable with the board--stopping, controlling your speed, and turns--and how to fall properly--yes this was part of the lesson. Snowboarding has a great learning curve and is a blast
