My story is quite similiar, though I was working in theoretical ecology. Turned out that I could handle the computers we were working with and their linux distros better than anything else. I went on for another 2.5 years and then quit. I aquired he LPIC-1 and LPIC-2 certificates from the Linux Professional Institute, worked as a pure Linux sysadmin for half a year and am now working as a sysadmin for Windows in Linux in my 5.th year.
Where I live you need at least some kind of certificate (or some on the job experience) and the will and ability to learn. In my experience most companies that are working with Windows will be quite happy to hire someone who doesn’t shy away from the terminal and/or cmd.
I have an Asus Eee PC from 2009 running Puppy Linux (as a secondary device).
As already pointed out you will need a leightweight distro and desktop environment.
https://distrochooser.de/ (available in English) can help you find the right distro, it takes into account the age of your device, your Linux knowledge, use case and a lot more.