Here are some thoughts for your K.C. to Austin ride.
In April 2005, I did a tour with two buddies near to your start and finish points -- we starting in Austin and finished in Abilene, Kansas. The objective was to ride the routes of the old Texas cattle trails, primarily the Chisholm Trail, which ended at Abilene. Our route, which was on low-trafficked highways, went west from Austin through the Texas Hill Country, taking in Johnson City to Fredericksburg. From Fredericksburg, we turned north on Texas 16 to Comanche, US-67 to Stephenville, US-281 to Jacksboro, and Texas 59 to Bowie. At Bowie, we got on US-81 and rode it into and across Oklahoma to Wichita, KS. US-81 was built on the Chisholm Trail route. From Wichita, we rode Kansas-15 to Abilene. We camped about half the time and stayed in motels other nights. Camping is often available in town parks.
The route has many interesting and historic sites -- the LBJ Ranch: Lukenbach, Texas (of the country music song fame); several Texas museums, including the Dr. Pepper Museum in Dublin, TX; Chisholm Trail museums (Ducan, OK, has a great one), Caldwell, KS, wild West history; and the Eisenhower Library and Museum in Abilene.
If taking this route, you might want to consider riding from Austin, since the winds are generally from the south. A couple of days we had unplanned 100+ mile days due to strong south winds.
If you aren't interested in the above route, an alternative is to head southwest from K.C., to Lawrence, Bladwin City, or Ottawa, KS, to ride the Prairie Spirit Trail from Ottawa south 59 miles to Humbolt, KS. Continue on US-169 to Tulsa, OK., then follow state highways or 2-lane US highways on to Austin. I rode that area on my first tour from the Texas gulf coast to Lake Superior, generally winging it as far as roads to take and it worked fine.
Whatever route you take, I'd suggest avoiding May and June -- prime thunderstorm and tornado season -- and mid-summer -- hot and humid. April and September are prime times.
Don't worry about over-planning the ride. I generally use state highway maps for determining routes and AAA guidebooks for lodging and campground information. Preliminary itineraries I make usually change during the ride due to weather and information from locals on better routes or things to see. Adventure Cycling's Companions Wanted site is a good place to advertise for people to join in the ride.