The issue with your question, I think, is over the exact meaning of the words "best", "basic", "web apps", and "popular".
By many measures the best and most popular stack would be mysql, php, html, css, and maybe a little jquery sprinkled on top. It powers an enormous amount of the web, it allows very rapid development, and it's about as cool and hip among the hacker news crowd as a cod liver oil enema, and with good reason!
Of course, you can improve it, but you need to figure out what metric you're looking to improve it on. If you rule out PHP or jquery or whatever, then other answers start to look like the most popular.
> Seems like React frontend
React has a lot of buzz, and it widely used for new projects trying to build web apps with heavy client-side functionality. Of course, there's simply an enormous amount of Backbone, Angular 1, or random jQuery client-side apps out there, plus an even more enormous amount "traditional" webapps with minimal client-side functionality (like hacker news). You have to define your search quite narrowly to make React look like the most popular tech.
> perhaps Vue
In the last couple of weeks Vue has probably got more buzz in terms of people talking about it on HN and /r/javascript than React, yes. From a certain point of view that makes it more popular than React; from basically all other points of views it's much, much less popular. Then again, why do you care about popularity? The wisdom of crowds is probably least useful when judging hype-driven popularity contests.
> and Node being the popular backend?
For small hobby projects among people who mostly know JS and have no particular reason to choose anything else? Yes. And low barriers to entry mean it's used in a large number of projects.
On the other hand, in many ways it is an objectively inferior backend. And in others it's objectively excellent. It really depends what matters to you.
> Is there a site that keeps track of [...] how their popularity progresses?
Depends how you want to measure that. You can use google trends, or compare github stars, or npm downloads, or the number of topics posted about it on /r/javascript, and get different answers.
Realistically though...
...none of it matters. Any vaguely functional stack is good enough; the odds of your project failing because you picked Rails instead of Django, or Mysql instead of Postgres, or Coffeescript instead of Typescript is nil. What does matter is that you pick a vaguely functional stack and start writing code.