Ok YOU ARE AWESOME, in advance, for offering up any tips you can. Here is the deal:

I plan on moving out to Portland, Oregon from Chicago Illinois

Yippee for me!!!

Its gonna be me, a cat, a bike rack (very sturdy, or at least should be since I opted for an upgraded model) and a driving companion, my mom who is 64. No trailers. Just what I can fit in the car and will have the rest shipped.

I plan on the trip taking three days, staying in a motel for 2 nights.

I have a 92 Honda Accord 164000 miles. Pretty ok car. Will get checked out before I leave.

What is the best route that would be easiest on my car to avoid steep grades?

Chicago toward Minesota, North Dakota, Idaho?
OR
Chicago toward Iowa, Nebraska, Wyoming, Utah?

Mapquest suggests I use the last option-Chicago, Iowa, Wyoming, Utah.

How is the route in terms of steep grades and mountain driving? Is it going to be really hard on my Honda?

Also, anyone who has done this particular route before, Any places I should not plan on spending the night in? Looking for cheap and safe.

Thanks again for any help and tips.