See for example NPM:
||Start with 1.0.0
|Backward compatible bug fixes
||Increment the third digit
|Backward compatible new features
||Increment the middle digit and reset last digit to zero
|Changes that break backward compatibility
||Increment the first digit and reset middle and last digits to zero
Anyway, with normal software these days (not libraries) it’s popular to increment main number when the new major version is released, the second number for smaller releases and third number for bug-fix releases.
This is more-less how Firefox works - but they use second number only in ESR channel (for example 78.3.0esr) because it often adds back-ported features. And the last number is for fixes, for example the last 80 was 80.0.1 which was fixing some bugs.
Regarding your addon, you can use the same pattern - keep it short 1.0, 1.1, 1.2 etc. and if there is serious issue, fix it with hotfix 1.2.1 and then continue with 1.3.
And yes, I would say definitely start with 1, not 0 .