Well looking at the map, I'd take I-65 southwest to I-40 then west on that. The disadvantage to that route is Oklahoma City, not a major problem. Then at Flagstaff take 89 north.
Otherwise you could take I-70 all the way west to Denver then south on I-25. The problem with that is St Louis and Denver, both I try to avoid.
We greatly prefer the North Rim but there are others who like the South Rim. We like the minimal crowds. You'll find a lot of the trails almost devoid of other people. And there are many back country roads. If you want reservations in the park you better make them early also be aware of the opening dates for the North Rim. Otherwise it's boondocking in the National Forest around the park or FHU in Jacob Lake.