Hey man, I'm a similar build to you, 5'11, 79kg (that's 174 lbs in your imperial system), and size 12 boots. Bought my first board around this time last year so maybe I can add a bit of insight.
You definitely want to look for a wide board, although you might get away with a mid-wide board in a large size.
I ended up getting a Ride Machete 157W (based partly on recommendations from this forum), which I have found to be a great all-around board. When I got it, I was just starting to do black runs (slowly). Since then, I've got comfortable on most/all black runs and am learning to do a lot of freestyle stuff. It handles the icy hardpack stuff at home (NZ) well and it handled pow really well at Whistler too. It's a little on the stiff side for presses, but you can't have everything (it's mid-stiff). You would probably be a bigger board size than me based on your height/weight (probably the 161W in the case of the Machete).
Already decided my next board will be a Never Summer Proto CTX 155. It's listed on the NS site as more freestyle oriented but the consensus on the site here seems to be that it's a very good all-around board.
I can't emphasise the importance of the right boots enough. They were the first thing I bought, even when I was still using rental boards. Had a pair of Salomons which were OK but I only got them because they were cheap. Got some Burton Rulers this season and they are a great mid-stiff all-around boot. Comfortable, no breaking-in period, perform well and durable. Another advantage is the imprint reduction... so my size 12 Ruler fits like a size 12, but it has the footprint of a size 11. Which I find makes tweaking binding settings a bit easier (most XL bindings are for size 11 and up) and reduces the risk of toe-drag for bigfoots like us.
Anyway, for bindings you'll be an XL or an L depending on the manufacturer (some don't do XL). Try and get something that matches the stiffness of the board, but there's a lot of good stuff to choose from here so you should be able to pick up something pretty good. I've ridden my Machete with Union SL and Union Atlas bindings. Not overly wild about the durability of the Atlas bindings (mine were starting to show a lot of wear on the ankle strap after only 2 weeks riding). Maybe I just have a tendency to break stuff, I dunno. The Burton Cartels are a pretty popular mid-stiff all-around binding so you might want to investigate them.
Anyway hope that helps. I don't know nearly as much / have as much experience as some people on this site, but I definitely love the Ride Machete.