Hi from the workshop of John Roberts
Building a basic wooden go-kart is great for you and your children. The idea of creating something that will give them lots of fun and in addition can help with your DIY skills too. My first go-kart I made was with small lawn mower wheels, which the children found hard to push and never had much free wheel momentum.
Also choose a good type of wood for the frame as my first attempt after a few days left out in the lovely UK weather rotted and snapped in half, leaving the children not very happy with their dad.
I have now made quite a few go-karts over the years and have found that the best wheels to use are silver cross wire spoked wheels on a steel axle, which are very light weight. They are very good because you can remove each wheel from the axle with a simple lever on the center hub.
These wheels are getting hard to find on the old style Perambulator. My kids are always surprised when old age pensioners say "I had one of those when I was your age" and not really taken on board how far back the traditional go-kart goes.
If you have some scrap wood you just want to use that's fine maybe your children would like to paint it when its finished I know mine did. This go-kart I will show you how to build is from a old silver-cross pram frame and wheels
Steering is important of course too, there are two types really by feet or rope.