Keep your name private
I asked my teen daughter what one thing she thinks is the most important thing she has been taught to keep herself safe on the internet. Her response: not to tell anyone her name.
I can add that when she is using a chat room, she is not to stay chatting if someone she does not know (as in someone who is not in her class at school or circle of friends) comes into the chat room and starts to chat with her and her friends. Even if someone she knows invites the person, she knows not to chat while the unknown person is part of the chat.
It is sad but true that every case of child abuse that I know of personally has involved either a family member or someone who is a close friend of the family. The internet makes it so easy to make friends and become familiar with people. Trying to teach children to see everyone as a threat does seem unfair but the only real way to make them aware of how close and innocent danger can appear to be.
In addition, every user of the computer has their own login details and none of the accounts used for surfing the internet have any admin. privileges.
Browsers are also set up to not display or download any third party content, neither images nor scripts.
As a final security measure, the hosts file is kept up to date with all requests for 'banned' sites sent to 127.0.0.1.