As often seems to be the case, it depends. For the Oregon to Ontario route, you may want to start on county roads until you cross the Cascades. From there to the midwest, you can probably just go for the smallest road that gets you where you want to go. For example, when you have a choice of interstate, U.S. route, or state route, take the state route; if there's no state route, go for a U.S. highway; and when you get to parts of Wyoming where the interstate has taken over the old highway, you may have to ride the shoulder for a while (or divert 50-100 miles north or south to the next road).
Adventure Cycling routes take you on just about every available type of road, but there's rarely a problem with traffic, and a bike tourist gets acclimated to traffic as (s)he rides. Where it does get tougher is around larger towns and cities, but there's more likely to be an alternative when the population increases. On the flip side, U.S. 287 from Rawlins, WY to the Tetons is a nice road, lightly trafficed, with good sightlines, pavement, and grades.