But now with the end of Windows 10 looming, I need to upgrade a family member’s computer to Linux.
Why?
Did they ask for Linux? Do you have authority over them?
So this needs to be something that both is not going to break on its own (e.g. while doing automatic updates) and also won’t be accidentally broken by the users. ... There’s no way I’m going to be able to handle long-distance tech support if things break more than once in a blue moon.
Issues appear. I would be more focused on setting up remote access than choosing a distro.
I'd choose something LTS that has been around for a while (Debian, Ubuntu, RHEL-derivatives, SuSE if there's a freely-available LTS, etc.).
If you are not against the use of Google products, ChromeOS devices are about the best well-designed low maintenance operating systems. (Not Flex, a ChromeOS device.) But you would be sacrificing Firefox and LibreOffice, which might not be an option. (And technically, it's running a Linux kernel, if I remember correctly.)