Yes, that should work fine. Normally you don't see many compatibility issues between a Motherboard and a Graphics card. In this case, it's compatible and will work fine! Enjoy the 1060, I've heard great things about them.
It supports the 1060, but the "full potential" part depends on the Processor. Your motherboard supports any Processor with a Socket LGA 1155. Intel only, So any AMD processors won't work. I dont think Skylake processors will work since the Socket isnt LGA 1155, i think its LGA 2011 or 1151. If I were you, I'd look up "Best gaming Processor for LGA 1155" and get an idea of what you'd want. Yeah, its a bit outdated, but if you get a good processor you won't notice many issues. Intel i5's and I7's would be perfect if you can find one within your price range. Make sure its LGA 1155 and that its not a S or T model (dont get an I5 3450s, since 's" basically means slower). But do some research on gaming LGA 1155 processors and you should be able to get an idea.