Finally a thread that I can provide some useful information for instead of being the guy asking all the questions. I have a bit of knowledge in the area being an AASI certified snowboard instructor.

Boots:
Getting comfortable boots is very important. It will ruin your whole day on the slopes if your feet hurt. I would recommend getting boots thats you have tried on first. Put them on, lace them up tight and walk around in them for a while. In cheap boots, the foam will sometimes tend to pack out over the day and you have to keep tightening them as this happens. I would recommend boots with a removable liner as they usually give a more snug fit and are easier to clean/dry.

Bindings:
Fairly inexpensive bindings should be fine for you right now. The biggest differences between normal and expensive bindings are the wieght and the adjustability. There are differences in the strength, stiffness, feel, etc. but as a beginner, you wont notice these very much yet so you dont need top of the line bindings.

Board:
The type and size of the board you get depends on a few things. These are your weight, your ability level, and your style of riding.
Length:
Shorter boards are easier to control because there is less swing weight. Longer boards have more effective edge in the snow meaning they hold an edge better.
Stiffnes:
Soft flex boards are very forgiving and easy to learn on. Stiff boards are good for carving but can be very unforgiving.
Width:
Narrow boards are good at transitioning from one turn to the next. Wide boards are good for powder or people with big feet. Unless you are going to be riding a lot of powder, you want the narrowest board you can get depending on the size of your feet.
Base:
Extruded bases are cheaper but are a little bit slower. They are easy to repair though. Sintered bases are a little more expenseive but are faster and more durable. Slightly harder to repair though.
Construction:
Cap construction is where the topsheet rolls over the side and come all the way down to the edges. Sidewall construction is where there is a strip of p-tex between the topsheet and the edge. Some people swear cap construction gives you better edge hold, some people swear sidwall give you better edgehold, I cant really tell a difference. Just different ways to put the board together.
Sidecut:
I would recommend getting a progressive sidecut wich means that the radius of the sidecut is smaller at the back of the board than the front. This makes entering and exiting turns much easier. Although riding switch (backwards) is a little bit harder. Most modern boards have this unless you get a true twin-tip freestyle board.

I'm assuming from what you said that you've been a few times and are starting to get it but still have a lot of improvement to go. And from what I know about you, I'm guessing you probably aren't the type thats going to be going into the park and doing freestyle stuff too much. So based on these 2 assumptions, you're at a hard stage to buy a board at because you want one that is easy to learn on but also one that will allow you to do what you want when you get better. I would probably recommend you go for more of an intermediate level board because they aren't that much harder to control and when you do get better, you will be much happier with a slightly stiffer, longer board than a beginner board would be. For length, I would probably get something around a 157. I've never really liked the guidlines that people give of getting a board that comes up to your chin, or up to your nose or whatever, because height has nothing to do with the length of the board you should ride. Your weight is what you should consider. A snowboard can be thought of as being a leaf spring and its very important to get one that matches your weight. When a snowboard is on its edge, it is bent in the middle, if you are not heavy enough to bend your board in the middle, it will be very hard to turn. If you are too heavy for your board, it will bend more than you want it too and will wash out and be very hard to hold an edge.

http://www.the-house.com is a very good online place to buy snowboarding equipment. A lot of the stuff they sell on there is last seasons models and they have very good prices. They also have some package deals there where you get a board, boots and bindings together for a discount. I got my last board there and was very happy with the service. It got to my house about 3 or 4 days after ordering.

There's a lot more I could say but I guess I'll stop now before I bore everyone too much. Feel free to ask if you have any questions on brands, prices, setting up equipment, etc.