Well... the Kano distro is pretty good for "I'm gonna learn how to type and move around the computer". [1] They have a build-a-computer kit and are coming out with a screen soon? It's a little old for my son, though. It really wants you to type things which is great except he can't read yet.
A colleague of mine had a lot of success with Edubuntu. [2] Her six-year-old is a whiz at the command line. Again with the keyboard use, so not quite appropriate.
I'm still looking, basically. He likes clicking around and seeing that he's having an effect on things, but he usually ends up at YouTube, which isn't so great.
[1]: kano.me
[2]: https://www.edubuntu.org/