First of all, you are almost my exact size. I started on a 143 and my current freestyle board is a 141 and my freeride/powder board is a 145. I prefer the 141 for general all-mountain shredding. I find it to be playful and easy to turn, yet long enough to be stable at higher speeds. For you, I wouldn't recommend going any lower than 139 because it won't be very stable once you start cruising. With that being said, you are big enough to ride women's gear. Stay away from youth gear - I have found that it isn't made as well.
How long a board lasts really depends on many factors. How hard will you be shredding? How many days a year do you plan on going? Will you be riding mainly on groomers, or will you be exploring the park/trees? Do you like having the newest equipment? I rode my first board for one season (about 20 days), then put it aside because I wanted a more responsive board. I could easily have used it for at least one more season, but I also like new gear and really wanted to try out something better.
For a board: look for something that comes in your size, since not all boards are made that small. Definitely look for something that can handle all-mountain, but you might want to try an all-mountain freestyle board, which would be a bit softer and thus easier to learn on.
It isn't necessarily stupid to get matching bindings, but it isn't necessary either. Just don't tie yourself down - look for the best binding for the best price and you'll be happy.
Since you're in NH, you'll be riding a lot of ice. Consider getting a board with magnetraction or Vario Grip, which will help you hold an edge in icy conditions.
Boards from M3, 5150, Lamar, LTD, and Avalanche are lower quality than boards from Ride, Rome, K2, Burton, Never Summer, Gnu, Roxy, etc. They won't last as long and won't grow with you, but if money is tight they would be okay to learn on. For me, finding the right board was a trial and error process. My very first board was an Arbor Eden, which I found very hard to turn. In a panic after days and days of constant falling-leaf, I bought a second board: Ride Rapture. I was linking turns easily the first day I took it out. Then this summer I decided I wanted (didn't need, but really wanted
) a better board, so I bought a Never Summer Infinity-R. Love the board, but it's just a tad too long, so I also bought a Gnu B-street. Now I'm happy. But it took me a while to figure out what kind of equipment best suits me. I guess the moral of the story is this: buy a decent board if you know you'll be committed to learning, but don't worry about buying the very best board out there. Eventually you'll be ready for an upgrade and at that time you can demo boards and find one that suits you best.
Some boards that are very popular with beginners because they are quality boards that will allow you to progress for several seasons are:
Atomic Fallen Angel (the Tika might also be a good option, I just don't hear much about it)
Ride Rapture or Solace
Never Summer Pandora
Look around on websites like eBay, Sierrasnowboard.com, usoutdoorstore.com, dogfunk.com, rei.com, and evogear.com to find last year's gear on sale for 50% off. You should be able to get a nice board for a decent price, but you'll have to do some searching. That, or you can wait for another month or so when some of this year's gear will begin to go on sale.
Good luck and have fun finding your board!