You definitely will need something like a 28-300 to get those sweeping vistas, particularly if it is mid day, since the haze in canyon will muddy shots. I would think nothing more than 200 mm would be perfect.
Bring telephoto as well as wide angle. While everyone else is grabbing those vast vista, you can single out a distant peak or tree or condor. 300 should be plenty. I brought my 50-500 and was not disappointed. I have two bodies so wide angle on the tripod and telephoto hand held https://lonestarnorth.ifp3.com/#/gallery/az-grand-canyon/grand-canyon-3959-64/
I was at the South Rim two years ago (in October) and brought my 28-75 on my D3000 and 70-300 on my D3200. I used both cameras (make that lenses!). I used the 28-75 for the vistas (and there were a lot of them) and I used the 70-300 to isolate parts of the photo. I shot a photo of a dead tree with the canyon in the background; I could only take that shot (and make it work) the 70-300.
Telephoto lens. Do I need to take any thing over 70-300mm for long distance shots?
You're looking at the world's biggest hole above sea level. Any lens you can find and use will give satisfactory results if used properly. The time of day will be more important than any focal length as the direction of the sun determines what colors the canyon shows. It is very difficult to miss a shot of the canyon. What ever you decide to shoot should be your best effort. Experiment, try different lens. Enjoy it, the size makes it worth seeing.