I have started a new project in which I would like to use React and Rails. This project is on the small side and will require some basic interactive UI, hence React. As far as I know there are two ways I could get started with this:
For a small project React-Rails, https://github.com/reactjs/react-rails, is great I have used it in production the last year on 2 sites that get about hundred thousand visitors a month and I haven't had any issues.
That said if you want to use Redux, React-Router or Flux don't use React-Rails go the API route.
My rule is if you are just using React components then use React-Rails.
If you are doing a Redux, Flux app then just make a frontend app.