Which version of Ubuntu should I use?

If you are new to Ubuntu; always go with the LTS. as a general rule, LTS releases are what people should install. 19.10 is an exception to that rule because it’s just that good. an added bonus is the next release in April will be LTS and you can upgrade from 19.10 to 20.04 then tell your system to stay on LTS releases.

Which Ubuntu version is most stable?

16.04 LTS was the last stable version. 18.04 LTS is the current stable version. 20.04 LTS will be the next stable version.