Best dual channel router to buy?

I'm confused by all the routers out there because of all of the types sold, "G", "N", and "AC"?

Do my wireless devices have to be, for example, N compatible, or G compatible or AC compatible?

I currently have Verizon DSL, slow but all that they offer for now in our area. I have a cisco valet (single channel router) now that poorly distributes wi-fi to all areas of our home, and the router is centrally located.