You're on the right track!
The quickest route per MS Streets & Trips is:
I-35 to Wichita
I-135 to Salina
I-70 to Denver
I-25 to Cheyenne
I-80 to just north of Coalville, UT
I-84 through Ogden (note: you won't be going through SLC but, rather, just north of it) and Boise to Stanfield, OR
I-82 to Ellensburg, WA
I-90 to Seattle
2200 miles
Please check out these great winter driving tips! I would suggest having chains and knowing how to put them on, just in case.
Something scenic? I've driven most of that route....the leg from Washington state to Denver....and I found the whole route pretty scenic. Well, unfortunately, you're not going through a very scenic part of Idaho. But I just always enjoy the changing scenery whether or not a particular area is scenic or not. It's amazing how diverse our country is.
I live in Washington state. If you'd like any advise about living here, and suggestions for weekend trips once you get settled in, let me know.