Both are valid options and there is no single "best" or "worst".
If you learn React first, you'll find that there are a ton more resources about it. And many of the things you will learn while learning React, will also easily transfer to React Native. On the other hand, the web has quite a few idiosyncrasies of its own.
(Fwiw, I have a post titled How do you go from React to React Native? which you may find relevant. I also have a couple of posts on animations.)
If you learn React Native first, there are less resources but it's not as big of a deal. There are no web idiosyncraties, but there are mobile idiosyncrasies — which you'll have to deal with if you want to do RN anyway, so if the goal is mobile apps, starting with RN might be cool, too.
It looks to me what you're asking, though, is more along the lines of "How do I learn RN best". Learning can be fun, but it can also be daunting and you can feel like you don't know where to go next, or even what to do now. So this is my advice about learning itself:
Relying on tutorials too much will only get in the way of learning. Instead, go through the official docs and the official tutorial, maybe follow a tutorial or two, but then, instead of finding a tutorial for everything, pause.
Following tutorials is good to get an initial idea, but terrible for retaining knowledge. Practice, on the other hand, helps you solidify the concepts and knowledge in your brain. Come up with a learning project, and go about making it.
You might encounter things that you don't know yet—and it's perfectly fine. Searching and reading about things in the context of a specific problem likewise does wonders to understanding.
Shmulik Kaminker
I think that react.js is easier to learn because it has nothing to do with the mobile world.
If you come from web development and you have knowledge of css, a little js and html it will be easier for you to understand the concept of react.js.
Although I did the reverse process: first I learned react native after I had a year and a half of experience with ionic, and because I was excited about the react platform I decided to develop with it also on the web.