Just for a contrary viewpoint, if I were stuck at the South Rim with only one lens, I think I'd go for long, not wide. A wide lens will give you a good record of the place, but you might wind up with a "bin there, done that" shot that looks like everyone else's. A long lens would offer an endless variety of shots extracted from the whole.
Besides, I'd go for the North Rim, not the south.
Peter