With a budget like that you can pick up some great gear...but just because it costs $600 doesnt mean its what you need. There are a lot of Burton haters around here but burton makes a great board. They're just over priced IMO. Rome makes great gear, I just ordered the 08 Rome Agent and some 08 390 bindings. Its more of a park board though, so I wouldnt suggest that since you're looking for more of an all mountain board. Look in to the Burton custom X or maybe the Capita Photo Fetish, those are great boards. I hear atomic makes great boards too but i have no experience with em, you'll have to ask snowolf about that.
As for sizing you could go from a 156-161 i think(for an all mountian board) and depending on personal preference...any where in there should be good. Someone else will correct me if i'm wrong i'm sure.
Binding...Union, Rome, Burton, Drake....all good bindings. Rome is more park oriented, look in to the Burton P1. But also remember that Burton has a different mounting system than other companies. Union makes a great binding too...lifetime warranty I think and I've never heard a bad thing about them. Dont know much about Drake but a lot of people ride em.
Boots...just try em on at a store. Whatever fits you best is going to be what you should get.
As for your shins, sounds like shin splints to me. I used to get them during football and track, and thats just something that happens. Not much you can do, stretch and take care of your legs. I'm sure it has something to do with your stance as well, snowboarding puts quite a strain on your legs.
Hope that helps a bit.