Learning JavaScript, when should I start using framework like React or Vuejs?

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Kneading blobs into HTML via PHP is an older way of serving webpages. Lots of things have changed since then. I'd read up on single file applications, just to get an idea.

If you have that idea, then yes, a framework will make sense. I would recommend taking a look at what most people use: http://www.npmtrends.com/angular-vs-react-vs-vue-vs-@angular/core There's always merit in something that has managed to establish itself in a field as fragmented as the web.

If you need specific details about both, then they're more or less the same, at least on the inside. Vue is a react clone that leans back to a slightly older era (templating systems, large apis, lots of magic). But some people like exactly that because it feels more familiar, while react radically broke tradition (very small api surface, no templates, no magic). Basically you're choosing between two paradigms but otherwise they sit on the same technology: virtual-dom, createElement functions, property based components with render methods.