I created http://benchurch.me/hackersearch a tool to search who's hiring threads using react and found it to be a great starting point for jumping off into the library.

It was simple, had a single external data entry point, was a suitable use case for diving into functional paradigms and has a lot of room for extension in the future as I continue to learn

You can see the source here if you'd like: https://github.com/bechurch/HackerSearch

Build something useful, which will have a real use case for you.

You put more motivation in a product you know it will be used by someone, like you.

A slack clone using firebase as a back end could touch on a lot of topics that would help you learn react inside and out - components, state management, routing, interacting with a server (ie firebase, but avoid the firebase-react library so you can architect things yourself) and more.

It's important to have a convention of doing apps in React, my one is available for free at https://www.reactjs.co :-)

Scratch your own itch.

you must have really itchy balls