For our security fixes, we recommend the lowest non-vulnerable version that is compatible with their project.
We do not run any tests of our own, but instead we would tell our customers that we recommend they write their own tests for their functionality to ensure version upgrades are not breaking their code.
In most languages, a minor (1.1.x → 1.2.x) or patch (1.1.1 → 1.1.2) release is considered “non-breaking”. Whilst a major version (1.x.x → 2.x.x) contains breaking changes.