Do you or your son have a preference over Windows 7 or Windows 8?
There is quite a (visual) difference between the two, with 7 being similar to older operating systems (start menu, text menus, etc.) while 8 is more similar to 'apps' and slightly similar to some aspects of OSX as well.
I'd probably stick with win8, given their situation. 4GB is definitely enough as well.
We have no preference on an OS because no one in our house uses a PC so everything would be new to us. Even the old PC that we got from his grandfather has only been used a few times because of the lag problem with Minecraft so my son is not used to PC (it has windows 7) Anything that is closer to an Apple OS would be an easier transition for us as now he uses Minecraft on our Mac.