Correction to your question: React is view only and Angular is a framework (not just view).
Now let's have a look at each of the frameworks you are considering :
As you said Meteor is good for MongoDB based (realtime) apps. No doubt Meteor is awesome, but it's also a full-stack solution. That means it doesn't fit into a different tech stack. It's itself a platform which utilises Node.js and MongoDB. So, I were you (with this particular use case) I wouldn't start with Meteor.
A lot of production apps have been built with Backbone in past. But I am not sure about the current state. I don't see a lot of development in Backbone. So, to be on safe side I wouldn't go with Backbone.
As you mentioned Angular 1 & 2 are completely different. Although Angular 2 is written in TypeScript, you don't have to worry as it supports ES6, Dart etc.. So, Angular can definitely be an option. But there are some concerns regarding whether Angular is deviating from standards. For example, see this answer by @EisenbergEffect, creator of Aurelia. I will suggest you to try Angular 2 and see if you are comfortable with it.
Well, React is a library and serves as just the view layer. But most production apps (including Hashnode) that utilise React also use an architecture called "Flux". So, React + Flux can be a great combo. Also JSX is not at all hard. It's just a way of describing how your DOM looks at any point of time and is very similar to HTML (with a few gotchas).
If you go with React + Node, you can do Server Side Rendering and build isomorphic apps (which is a big deal). I don't think other frameworks support this. The community support is huge and you will definitely get a lot of help from other developers.
At Hashnode we have been using React which is working out really well for us. So, I will say React is a great choice and is definitely worth trying out.
I have heard good things about Ember. Since I haven't worked with it, I can't comment.
TIP : You should also try out Aurelia and Vue.js.
Conclusion
IMHO, go with React. But I would love to see others' perspective. You should read all the answers and take an informed decision.