Would you like to install a operating system that is cheap (free) and kids can browse and play in the internet without slowing our computers with viruses. Sounds like you?
Honestly ask yourself two questions to get the answer.
Do I have a pretty fast computer or is it a small netbook?
If you have a fast, newer computer I would recommend on the Ubuntu, Mint distributions. Very good Distributions that are easy to install and configure to the kids liking.
Lets say that you bought them a little Netbook. Perfect for browsing but slow. Well in that case lets ask another question. What are the kids going to do? If they are going to browse all day websites and play online games I recommend Puppy Linux. A very fast, small Distribution that will look great on the little Netbook. Now, if your child wants to produce their own shows like, I-Carly then install the Cinnamon Distribution. Once you install the Distribution download cheese for their web camera and Openshot and Kdenlive to edit their videos and voila you just created a little movie monster. I don’t recommend Puppy linux for anything else that browsing due to sometimes having to figure out installations, “I had a few instances were I had to research tutorials to install certain programs”
I would also recommend asking the kids to install Minecraft with no assistance, make them aware of the tutorials on Youtube. Kids are amazing at this, plus they are fascinated at how much they can do with Linux.