Driving to Yellowstone from Southern California

[jlo]

Does anyone have experiences to share about their drive from Southern California to Yellowstone?
 
We are not sure from Salt Lake City, as to whether we should go up through Idaho and go in the West Entrance or go up through Wyoming and go into the Southern Entrance.
 
Which is an easier drive?
Are there any places you recommend as a must see?
Does anyone have a favorite campground?
 
We are also planning on going to Mt. Rushmore from Yellowstone. Again, does anyone have any advice or ideas to share?
 
We appreciate any thoughts.