your direct route is going to be fine just as you have it.
We like leaving I 80 at Rock Springs and going up 191 through Pinedale and over to 89 north up to Jackson. No problems with the road last year, but you know they like to work on roads in the summertime up there :) No grades to worry about.
We like to spend the night at Warren Bridge federal campground, about 20 miles west of Pinedale...turn into campground just before crossing the bridge. This puts us in a good spot for arriving at the Tetons around mid day. The campground has water and a dump station.