I have a Toshiba Satellite 300CDS (150 MHz Pentium MMX, 32 MB RAM, 2 GB HD).
I installed Mandrake9.1 on it (Mdk10.0 install fails with Perl errors). Everything's working perfect.
As for easiness, I use the Matchbox window manager. I can't imagine a simpler window manager for childrens (all windows are full screen), and it is lightweight-enough for this laptop.
See:
http://matchbox.handhelds.org
Write a follow-up if you need help.
Yves.