The way you make HTTP requests in React Native is with the Fetch API. In this video we'll talk about Fetch and how to work with promises.
At the end of the video you mention that fetch isn't available for the browser yet, but it is available for React Native.
If I plan on writing a web app, (that also serves as a Hybrid Mobile App), that relies heavily on API calls, should I just stick to $.get(), or can I start using fetch?
Ironically Fetch went live a few days ago in the latest version of Chrome. But if you want ANY sort of older support, definitely go with $.get for now.
Github has their fetch.js shim (which I used in the JSBin here).