Welcome to the forum.
That's a long trip and hard to predict weather and road conditions. I15 and I90/94 will be fastest imo. Check this before you go (click on the States for details)
I'll suggest the I-80 to The I-29 in Omaha ... Gets you out of the Mtns.& on the plains, the first day ... Then, miles & miles of miles & Miles ... Can't be helped ... carracar
Watch the weather and choose your route just before you leave. Then find a hotel along the way toward the end of the first day. You will have to go about 9 hours, unless you want to break it up into 3 days. Billings is about 8 hours away, and is the best place to stay along that stretch of highway, so that would be the ideal place to stop.
The I-80/29 route suggested adds 200 miles but, if the weather is problematic in Montana, then that's the best way to go. You just need to stay tuned and stay flexible.
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