How can I improve as a site builder for dealing with errors I don't know how to handle?
I'm not really aware of a way to improve your workflow. In general I would recommend limiting your usage to modules that have hundreds or thousands of Downloads by site builders, but that is not a silver bullet. And, sometimes you need to use that -dev module that has only 5 downloads because it will save you tons of time in development work on your project.

Everyone typically builds up a listing modules they are familiar with, comfortable with and trust -- build that list for yourself.

Something you didnt mention and I think is a larger problem than what you've outlined is testing module updates to an existing site that is using tried/tested modules previously. I'm more scared of things breaking during a large update (even amongst stable modules) -- then of experimenting with modules earlier in my site building process.