- The most important rule is that your recovery from backup procedure is working properly. - The second most important rule is that your backups are working properly. - The (distant) third most important rule is to always individually backup any text file you edit before you edit it.
Seriously. These are the most important rules.
Other pro-tips are to test any changes to remote access (SSH most importantly) before you close the session that you made the changes in. Also, schedule restore from system backup and restart before you make any potentially crippling changes to the system configuration. If the changes work then you can cancel the restore / restart. If the changes cripple the system it will (if you've followed rules one and two above) recover itself. Finally, if you can afford it, try to run at least one dev / test instance of each critical system. You can make changes, point a few test clients at the new instance, make sure it's working, then either make the changes to the prod system, or do the dev / prod swap-over.
The actual ways to achieve these rules varies depending on OS mix, hardware, cloud providers (if any), use of certain tech (are you using virtualization? Are you using containers? Are you using some form of orchestration tooling? etc.) and many other things.
The first two rules mentioned above, and the order in which they're mentioned, are by far the most important rules in sysadmin. Ignore them at your own peril ;-)
Good luck. Keep a level head, don't panic, and test your backups!