Cheapest chassis you can find on Craigslist, Marketplace or here will be sufficient. Do what OvalTech said and throw a predator on it.
Attempt to set it up correctly and focus on letting them have FUN at their OWN pace and let them get seat time seat time seat time.
Then if they love it... Find yourself a kart around 2010 or newer. They can be found with only a few races on them. You'll spend less than having them beat up a competitive chassis while learning. (You'll learn quite a bit too!)
I have no doubt the newer karts have innovations that make them moderately superior to the one you chose. Still, when it comes to handling, most say "tires tires tires tires". An engine, properly built, can make a difference, so stick with the box stock class. Right out of the box. The Briggs LO206 is a good engine/class to start with. I say that because your going to spend so much time learning to drive and set up the kart, worrying about somebody building a better engine is something you might want to avoid, at least until you learn the basics and your kid gets comfortable racing. It might look easy, but I can assure you it's not.