OS X 10.2.8 Jaguar is very old and you'll have a hard time with many things, including Internet access using this OS X version.
Most G4 PowerMacs can run OS X 10.4 Tiger.
The problem, if you don't already own a retail copy of OS X 10.4 Tiger, finding this and purchasing this now is going to be very expensive. More than Apple's original $129 OEM retail.
If you know someone who uses Macs and has had older Macs, could find out if that person has a copy of OS X 10.4 Tiger that you can use and install.
OS X 10.4 Tiger upgraded to OS X 10.4.11 is really your hope for having a decent Internet experience.
Especially with kids.
Here is the version you will need to install.
http://www.amazon.com/Apple-Mac-Tiger-10-4-6-VERSION/dp/B000BWZZLG/ref=sr_1_2?ie =UTF8&qid=1368125492&sr=8-2&keywords=OS+X+10.4+Tiger
or here
http://store.fastmac.com/product_info.php?products_id=100
Also, have you considered an iPad?