We have the following guide on how to perform upgrades: https://invisioncommunity.com/4guides/welcome/install-and-upgrade-r259/
However, there isn't really a best practice list outside of what I mentioned in my other post. I would recommend the below, seeing as you are so far behind in updates. Additionally, setting up a test install may be a good idea if you have a lot of customizations to test or simply want to test upgrading.
Before performing any core software upgrades, do some research of the third party applications/plugins/themes/etc... you have installed and see what is available for the most recent release. If you there are any that aren't mission critical, now is a good time to perhaps uninstall those.
When you're ready to perform the core update:
Turn your community offline.
Take a full backup (database and files). (for those reading who are cloud, you're all set here)
Disable all third party applications, plugins, and language packs.
Create an unmodified theme and set it as the default theme (ensure your administrators who are helping with the upgrade use that theme)
Perform the core upgrade. As you are so far behind, it may be a good idea to perform a manual upgrade (see guide above for more details on that). If any issues with the core upgrade, please create a topic here and someone will help you 🙂 .
Have a look over your community to ensure things went well. This is a good idea for the next step.
Once the core upgrade completes, you will want to consider looking at getting your third party items in line:
As you are coming from 4.4, you will want to setup the Marketplace integration and go through onboarding. There should be a notification to do this in the notification bell of the ACP (top right). This will step you through which applications/plugins/themes/language packs you have installed from the Marketplace or are custom (aka custom development you had done or installed from elsewhere).
You will want to upgrade each application/plugin/theme/language pack independently and then test before moving to the next one. This will allow you to tell what may be breaking and causing that break.
For third party items which have no compatible release with our core software you just upgraded to, be very cautious of enabling these but ultimately, enabling these independently of others is advised.
Done!
These "best practices" are really an extremely cautious approach coming from a rather old version. Point upgrades (e.g. 4.6.11 to 4.6.12), you likely would not need to be this cautious but I would stress item 2.2 (Backups) for any self-hosted client for any upgrade, no matter how small.