US-36, US-50, US-24, US-54, US-400 will all get you across. I've traveled each. Each goes through different interesting places, small cities and tiny towns, you kind of need a guide (even AAA will help) to know what to look for in each place.
US-36 and US-54 have the advantage of bypassing Kansas City.
Fort Scott on 54 has the "first" U.S. military cemetary, at least first in the present system. US-54 does go through Wichita, but that's not so bad as Kansas City for getting across. Just pay attention to the place where the speed limit drops to something like 35 MPH on a stretch that looks like expressway. You will want to leave US-54 before it dips down into the Texas and Oklahoma panhandles, that's where you pick up US-50.
St Joseph on US-36 has the start of the Pony Express and was a crossing and starting off place for some of the settlement trails to the Northwest. The route also boasts birthplace of sliced bread (Chillicothe) and boyhood homes or birthplaces of Walt Disney and a collection of WW1 and WW2 military leaders. All in Missouri.
US-numbered highways in Kansas are pretty good, even where two-lane. Most local drivers prefer to move pretty fast on these roads, and most are not afraid to overtake. Long haul truckers move fast too.
Kansas two-lanes have passing zones, keep right except to pass in these. They are like the old three lane highways, middle lane is marked and used for passing in both directions. Hogging the passing lane could get you a head-on collision.
Tom Test
Itasca Spirit 29B
