Wow, I'm in the startup world and haven't heard of half the stuff you mentioned. The other half is my bread and butter.
HN may not be the best place to get a sense of which technologies are worth using because it tends to mix the broadly used stuff with the new shiny that's just a flash in the pan.
I would start by asking how much it is you feel you should know about each of these technologies, and why. Nobody can or does know of every single tool or framework of service that's out there, let alone understand them in depth. But you can probably get "what it is, and what do most people use it to accomplish" in under 5 minutes for each one a client brings up. Then there may be one or two per client that are worth learning in depth.
For instance, github is just version control hosting for git. If you work with client code, it's probably worth your while to be able to accomplish basic operations in git, even if you don't master it yet. But knowing github beyond a basic understanding of browsing websites is probably not worth your time.
Similarly, if you're deploying software for a client that uses puppet and nginx, you'll need a working knowledge of both (skimming the docs lightly is a good place to start for a new technology - you don't have to memorize every detail but get a sense of what it's capable of and what the terminology is that is uses so that when you're troubleshooting you know how to ask questions and which parts of the docs to return to).
But if you're just writing a new feature for the client's application, or troubleshooting their database indexes, probably all you need to know to be productive is that nginx is a web server and puppet is a tool for automating server management.