When I was shooting Canon, my wide angle lens for landscapes was the 16-35 f4 zoom, quite good. to me, 16 is already really wide, I am more comfortable around 21-24.
Not many systems offer such wide angles for FF, for Sony Alpha 7 Voigtlander just came out with 10, 12, and 15mm lenses, for those who crave such lenses. For Canon EOS, the obvious choice is 11-14 zoom, which is beyond your budget, unfortunately. Samyang 14 comes to mind.