What do you use for a kids (ages 4-7) OS?

I have an old machine I want to stick on a desk in the living room for a wee one to use. I'd like to be able to have the internet to download stuff and then shut it off so they have fun games and content offline, but not endless scrolling stuff. Before I just started slashing away at a debian install I figured I'd ask here what you've used, the title is more geared towards me tossing a pre-stripped linux OS on it, but anything would be welcome as far as a userland application to accomplish things agnostic of the linux flavor.

*I was/am looking at edubuntu/ubermix to do this originally