You are pretty much exposed to a fair amount of climbing no matter which route you choose, as all east-west interstates traverse the Rockies. I consider everything east of the Rockies to be kind of a null, a big empty nothingness to be driven across as quickly as possible. So considering what happens as you go south to north:
1-90. Goes into some pretty country in western Montana and stays there all the way to Spokane. Grades pretty easy to handle. Fourth of July Pass east of Coeur D'Alene a trifle challenging, but not bad.
I-80. Probably the most direct route but Jesus, booooring and almost anti-scenic. 400+ miles of Wyoming desolation, a little bit of scenery through the Wasatch to Salt Lake, and then 600+ miles of Absolute. Nothing. to Reno. Then, Donner Summit (beautiful, but can be challenging in weather).
I-70. The prettiest route; also the most challenging as far as traversing the mountains goes. You'll have the choice of heading north via US 6 to I-80 or south through Vegas to hit I-40 after you emerge from the mountains.
I-40. Mostly booooring but scenery through New Mexico and eastern half of AZ can be interesting. A good choice if weather threatens. Pass crossings are gradual.
1-10. A whole lotta nothing. You drag yourself across Texas, then 4+ hours of desolation to Tucson, and 6 more hours of absolute nothingness (yes, that includes Yuma; Yuma is nothing) until San Diego. Gasp gasp.
My choice would probably be I-70 to US 6 to I-15N to I-80 west. It's one of the two quickest routes, and the Rockies crossing is a lot more interesting than on I-80.