I recommend Backbone as a first JS framework. As mentioned above, it contains less "magic" (and far less code) than any other framework of its popularity. You can read the source for Backbone in an hour and will likely learn something about good Javascript practices, and self-documenting code, in doing so.
Moreover, Backbone is a great example of MVC, the understanding of which is useful and highly transferrable to other (even non-JS) frameworks.
As many people are echoing in the comments, I'd go with React just because it's so easy to get started with. Once you get into it, the Flux pattern is pretty sweet although it's being morphed to use Relay/Graphql which are pretty creative.
Also, React Native is the new way they're proposing to build native mobile apps; definitely new but worth it to learn React in case this works out.
I would definitely push people towards learning Meteor. I know it's a full stack framework instead of just a front end framework but for rapid prototyping, it's fantastic. The community for Meteor is a bit hit or miss because it's so "magical" but it's worth a look too.
Disclaimer: I've only ever done about a week of Angular so I cannot compare features.
Angular really needs ui-router, lodash/ramda, and jquery (for more than just AJAX).
React doesn't need a router for many uses (extending existing sites), but does need lodash/ramda and an AJAX library. ImmutableJS is useful for both angular and react (as is rxjs/baconjs). For a beginner, I would simply say React, Reflux, Ramda, and jQuery will do 90% of the things. Learning all four of these libraries (they probably already know jQuery) will take less time than Angular and be more flexible if they want to swap one out later.
Finally, adding these is much easier with commonJS than the angular dependency injection (often on top of commonJS).
I like all the libraries that you end up having to use with React (and I end up using Lodash with everything anyway). I also think React is a better solution most of the time, but it requires knowledge of the JavaScript ecosystem to grab all the libraries you need whereas Angular does not. As a newbie it can be hard to identify not only what libraries you need but also what is the best of breed.
I've also heard good things about Knockout, but I haven't reviewed it. Ember is also popular; I've used it and prefer React.
Some people will say that it's unfair comparison because React does so much less than Ember and Angular. To that I can only say: Yes, and that's part of why it's better.
The reality is that Angular 2 is probably going to be the dominant framework, so if you don't want to learn Angular 1 then it's probably best just to wait six months to learn Angular 2.
To be honest, I started learning VueJS first (vuejs.org) and that got me into the line of thinking of MVC/MVVM. After I finished my project prototype with VueJS, I ended up going through an Ember tutorial or two and rewrote that VueJS app using EmberJS. I highly recommend EmberJS because of its painless upgrade process, strong conventions, and awesome community. Once it clicks, you'll be amazed by how fast you start shipping out features and building complex UIs.
