The most useful thing I have ever done to improve my squirrel hunting is to spend time at the range with a scoped 22 and a handdful of golfballs. The golfball almost perfectly mimics the size of a squirrles head (grey and fox) When you hit the golfball, it hops around and gives you another shot, and a slightly different angle and range. Once you start to hit golfballs with ease, it's pretty easy to convert that skill into headshots on squirrels.
Not sure if this will help you, since I don't think the terrain in Kansas is similar to Wisconsin timber, but I usually use "spot and stalk" for squirrel. Move thru the woods slowly and look for squirrels foraging or listen for them gnawing on nuts. Then, quietly sneak into shooting range. Depending on where you are hunting, you will need to decide it shooting up into trees is safe, otherwise you'll have to try and tag them on the ground.
Stand hunting is also effective, especially in the morning or evening.
We will usually sit for a an hour or so after sun-up, then start to spot and stalk.
Guns and gear
Either your double-duece or sweet-seventeen should be fine. I use mainly a .22. If a shotgun is used, stick with 6 shot as most of the shot will pass thru, and the remaining pellets will be easier to find. As for other gear, don't overlook the use of binoculars. Even it heavy timber, they aid in spotting the little bushytails.
And remember to have fun. Many hunters "grow out of" hunting rabbits and squirrels in seach of bigger game. But there is not many hunts that are as simply enjoyable than chasing bushytails