The following is a brief list of instructions for getting Ubuntu Netbook Remix (UNR) set up on an MSI Wind u100 in a reasonably child-friendly fashion:

1. Get the Ubuntu 9.04 ('Jaunty Jackal') UNR image and install it according to these instructions. Do not try 9.10 ('Karmic Koala') - at this point it's broken (which should come as no surprise to those who've tried Karmic).
2. Uninstall Pidgin and Evolution using Synaptic.
3. Create a user for each child who will use the device, and turn off unwanted priviliges - in particular "Administer the system". Leave WiFi connection privileges alone (kinda misses the point of a netbook if you disable that).
4. Install DansGuardian (and Squid and ClamAV) according to these instructions, stopping once you've completed Step 3 (i.e. before you start configuring WPAD).
5. Configure your system to use localhost:8080 as your proxy for all users according to these instructions.
6. Make Firefox proxy settings read-only according to these instructions.
7. Observe that everything stops working when you reboot. Squid isn't clever enough to pick up changes to resolv.conf that NetworkManager makes when it connects to a WiFi network. The fix is to create a dispatcher script in /etc/NetworkManager/dispatcher.d that restarts Squid when it receives an 'up' message. Seriously.

The dispatcher script I'm using looks like this:

#!/bin/sh -e

if [ -z "$1" ]; then
  echo "$0: called with no interfact" 1>&2
  exit 1;
fi

# restart Squid so it can see the new interface
case "$2" in
  up)
    /etc/init.d/squid restart
    ;;
esac

Anyhow, on the list of things to do is to figure out how to route all HTTP traffic through DansGuardian using iptables, so as not to have to depend upon Firefox and other apps honouring the system proxy settings.

I can't help but see a commercial product here: a remix of Ubuntu Netbook Remix, but designed from the ground-up to be child-safe. Perhaps it could even use a separate apt mirror, loaded only with child-safe apps? I mean, I got very lost several times figuring this stuff out and I do this sort of thing for a living.