+1 -- most of the comments are about minimizing downtime, which you should of course to do to the extent practical, but at some point, whether you're a one-employee company or not, if you have no internet access and your servers are down you have to keep calm and accept that there will be some downtime and it's not the end of the world. You may even be surprised how few customers notice anything went wrong (depending on the kind of service you're running).
The question is not whether your system will fail, the question is when.
Have proper monitoring and alerting in place.
But don't over engineer it, sometimes everything seems technically fine, but your support inbox will start getting user complaints.
Resolve the issue, figure out the root cause, make sure this or similar stuff won't happen, apologise to the affected users if necessary, and move on.
You'll learn waaay more failure modes of your application running in the wild, than just thinking about "what could go wrong".
It's a long game of becoming a better developer/devops guy, and not repeating the same mistakes in the future.