https://huntfish.mdc.mo.gov/fishing
https://huntfish.mdc.mo.gov/fishing/species
https://huntfish.mdc.mo.gov/fishing/get-started-fishing
https://huntfish.mdc.mo.gov/fishing/where-fish
The larger conservation areas with a admin building, classrooms, and so on, have small lakes and ponds for kids. What you'll find in Missouri will be lots of bluegill and largemouth bass, along with dang near anything else. You can fly fish for both, but for kids, bait and a bobber works great for bluegill. Plastic worms, various topwater and diving lures, and jigs are common bait for largemouth. In the Fall, I like to use a topwater such as an old school buzz bomber. I'm not much of a worm fisherman and I prefer fishing in the clear streams and rivers in the south part of the state.
There are community lakes all over the state with mixed fishing success. Many cities or organizations such as Lions Club have lakes open to public fishing. There are several Conservation Areas SE and South of Sedalia with creek and pond fishing.
The streams and rivers North of the Missouri tend to slow and muddy. South of the Missouri in the Ozarks Plateau you'll find clear streams with small mouth, goggle eye, largemouth, bluegill, red ear, just all sorts of fish. There are a few streams with self sustaining populations of rainbow trout, but they tend to get a lot of pressure.
Missouri has a 1/8th cent sales tax that goes to the Conservation Department, and it has been well used; our facilities and CA's all over the state are proof. The Conservation Department has a commission that is insulated from political pressure, probably as well as could be expected in a perfect world. We probably have the best department overall of any state in the union, it's certainly in the top two, maybe three at worst.
I live on the opposite end of the state from Warrensburg and I grew up in the SW part of the state, so my first hand experience out there is limited. Look around a little, you'll find more opportunity than you'll be able to use this year.