I'm finding myself reading through all the documentation, but I feel like I'm wasting my time. I don't know if I should just jump right in and start coding.
What's the most efficient way for you to learn new technologies?
I usually try to start with a nearly trivial problem and work my way through it, eg. right now I'm learning Polymer and started by taking the landing page of my previous startup (written in Django/vanilla-JS) and porting it to Polymer. It is slow going, partially because Polymer is really bleeding-edge (still in developer preview) and core functionality changed as recently as a few hours ago. But I've learned a dozen or more technologies in my career, and each one of them was through actually building something and wrestling with the framework enough to grok it.
Popularity has never been a significant concern of mine - most people are sheep who follow the crowd, and so if you have hard data and extensive experience, you will either a.) set the trend, so that they follow you or b.) have a big competitive advantage over everyone else. Most great products are founded by doing what everybody else is not, so if you do what everybody else is, you're automatically resigning yourself to mediocrity.
There's no substitute for having a concrete problem to solve, then hitting the docs, reading around and implementing a solution.
You'll also find out what it's like when things don't work, which is something you rarely get from documentation.