System maintanance of Gentoo can be very time consuming, and I would't recommend it for your kids' computer unless you can't find anything else that will work on that machine, which you probably will. Gentoo will be fast, but in many cases the diference in speed is not significant. Vector is probably a better option, I don't know much about it.
for a computer for children I would also consider Edubuntu, a variant of Ubuntu linux designed for children and the education system. It may be too heavy for your system, though, being GNOME-based. In this case I would suggest trying Xubuntu, which is another variant Ubuntu linux that uses the lightweight XFCE desktop environment and will work better on older computrers. I'm pretty sure you'll be able to add all the Edubuntu packages to Xubuntu after the installation.
If none of these options does the job well enough, ask again and I hope we'll find somehting better. There's a lot of chice in the Linux world.
