Bindings also come in sizes, but it's rather forgiving. Each company has their own sizing chart for bindings though generally large will be for boots 9+... Speaking of which I noticed you gave your shoe size.
The thing about boots is they have to fit snug. If there's extra space in the toes you're gonna end up curling them when laying onto your toe-edge and getting sore real fast. So although boot sizes are the same as shoe sizes, generally most people will size down by 0.5 or even a full size since most of us leave some room for our toes to wiggle in our walking shoes. Of course you also don't want your toes cramped either for obvious reasons.
As for specific boards/bindings to look at... I really can't help you.
When I bought my entry setup I bought nothing but clearance rack items of which most were already lower tier equipment from their respective companies; Ride Control board and Burton Mission bindings(I have to admit I like Burton ratchets). They were still better than the rental crap I had to use though.
My general advice is to look for a regular cambered board that's a bit on the shorter side of your ideal board length as you're starting out. Maybe someone else can point you at something a bit more specific.