The real truth: long gone are the days of just being able to "click-n-burn" a TC iso and have it boot with modern computers that barf on anything cd in nature.
But we do know some things:
1) Burners like Balena Etcher, Rufus and so forth DO a proper job of burning the iso's. It is NOT THEIR FAULT.
2) The iso's themselves are not suitable for booting on modern machines, unless you use techniques on them first, like using isohybrid. THEN, the burning tools will do exactly the same job they did before (doing exactly what they are told by the iso), but now have the ability to appear as a HDD instead of a CD to a modern computer, which modern computers don't like to boot from - either from a technical or security issue.
3) A modern machine wants to see a 64-bit iso anyway, so the only one you could would be the TinyCorePure64 versions. With isohybrid used beforehand.
3.5) There are other ways too, like using multibooters, which rip the iso apart, and lay down their own filesystem structure, and then rely upon YOU to massage into working to meet the TC specs.
4) BUT, lets say you are successful - well, that's emulating a CD environment. Most want to go beyond that and use a dedicated install to a "tce" rather than a "cde" environment.
Thing is, there are nifty tc installer tools available, such as tc-install-gui, but the problem there is sticks burnt by those aren't up to date enough to be bootable on modern machinery!
So - what I'm saying is that with TC and modern macinery, we've reached a point where you either have to have a lot of a-priori knowledge of how TC is supposed to work, or put in a LOT of time getting it to work, and that means you are on your own to figure out your hardware and operational specifics. And at some point, hand-holding in the forums just won't be enough - you'll need to do work on your own.
To be honest, coming from your background, TC on modern machinery is still not a click-n-burn way to joy. Kind of a catch-22: If you know, then you aren't asking.
THIS is why the emphasis is on the end-user getting enough linux knowledge in the first place to build their own bootable sticks manually with the distribution files, using your own bootloaders and config files and so forth just to deal with the modern gear.
So this isn't any sort of "fault" with TC. It's just that modern gear has taken the simplicity of the golden "cd" years away, and the user needs much more knowledge than they did before - even going beyond just typing in stuff from the forums and crossing fingers...
Honestly, I'd say stick to what you know, or if small is your thing, then maybe another distro, like antiX might be more suitable.
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