Which versions of Python should we target in the future?

I added GitHub CI but could only add 3.5 up, as 3.4 is end of life. (Tho I'm sure if we got creative with Docker containers we could sort that out)

But should we bother?

I would suggest 3.6+, as that's what Ubuntu LTS 18 has and 3.5 is EOL in 2020-09-13 anyway.