What solutions have all of you hit upon? Is there a kids' Linux distro which is lightweight and does the trick? What's best to run it on?
Many thanks!
How much effort are you willing to invest?
How much do you want to make their experience suck?
Are they asking for Linux or is that your idea?
How much of your concern might be managed on the router?
OK. My advice. Talking to your kids as autonomous humans is a better investment of your time than technology shopping. Reasonably good judgement doesn't come in a box. Ask them what they want and give it to them if you can
If you don't like iPhones/Windows/Chrome or moralize software licenses, that's you, not them.
It's just a computer. Just a tool for getting schoolwork done. Buy whatever and then spend all the time you saved with your children (times 10,000).
Good luck.
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Appendix 1: Porn
Your kids will see it on other people's screens even if they have no computer at all.