Sounds like you want Firefox Extended Support Release (ESR). ESR releases receive a major update only once every 10 months, but still receive the same bugfix and security patches as the regular releases. Also, when you do get updated to a new ESR version, you know that it's one that's already been supported as a regular release for 2 months, so there's very little chance of surprise problems.
The current version is Firefox ESR 38, which was released as ESR on 11 August last year. The next one is ESR 45, coming on 31 May, which will last all the way until 21 March next year.
Hope that helps you.