I picked up some "E machine" netbooks for my daughters (9, 5 &4) over the summer. They're running XP and seem to be fairly well built for the money (£199 each).
I did look at the Asus range, but some of them run linux, and this might not be idea for kids (confused the hell out of me!)
We got the emachines NAV51 netbook for travelling and its worked very well. £199 seems to ring a bell. 10.1 inch screen which makes the font a tad small for my eyes, but wouldn't have thought kids would have the same problem.
Its functioned flawlessly, wireless as well....i'd recommend it, bearing in mind i havn't got anything to compare it with.
Battery life is a bit limited, 2 hours i think but you can't have it all. 2 hours maximum mind. The only slight downside (IMO) is that the power supply is a bit minimalist, particually the cable to the netbook. Looks like you'd have to take care of it.
But otherwise, it gets regular use, boots up quick, works well on wireless....all in all, i'm happy.