I found this site a while back - basically it will ask you a bunch of questions on your usage of your PC, and will came out with a list of recommended distros, and a list of reasons why YOU could like or not like it.
There are some similar sites to this one, but since I’m not familiar with them, I won’t post them. They are simply DuckDuckGo-able though.
How bad is really bad?
AntiX is a good choice. Other option is a usb3 drive for each family member so everyone has their own portable AntiX on a stick.
MX is the related project with a more standard install and could be worth a look, the Fluxbox option should be quite light.
Each user could have a personal AntiX system on persistent usb3 and each system could have a bare metal MX Linux install. Just see what wins out via natural selection over time.
LXQT is another option for a full desktop environment that will run on a potato. If family members are mainly just users and you are admin, the base OS may not matter much. They could switch between a potato running Alpine and a good system running Fedora and if they are just logging into LXQT to launch browser, office, email etc the internal system plumbing is not gonna concern them.
I like your solution! Thank you.
About my computers: I have 2 1GB RAM laptops. One has 20-25 years the other one 10-15. I have tried Puppy and antiX in these. And I personally prefer antix on them. Another 4GB laptop that might be around 8 but is pretty trash as it was a gift from our bank (it was able to run Elementary OS, it was fine). A kind of old computer but with 4GB RAM (Think I have XFCE or Cinnamon Mint on it). And a big boy with 16GB and a pretty good CPU. And the oldest computers are used the least often (maybe once a year) while the middle computer might be used 20 times a year and the last one maybe once every week.
So I believe something like antix would work, but I’m not sure if the USB way would. Seems like they would lose their pendrives the second day.
I’d put the 1gb ram laptops to server/kodi/retroarch/something mode and focus on the three decent machines for anything that requires a modern web browser, or add some ram. Porteus might be worth a shot if you’ve not tried it and want to push the Firefox on a potato idea.
I don’t think this is a one OS fits all situation, unless maybe Gentoo.