If you want to learn Rails, you should choose a project that will teach you Rails. If all you're going to do with it is serve up JSON, then you're not really going to learn anything and will needlessly overcomplicate your app. Just use something like Sinatra in this case, Sinatra will get out of your way and allow you to focus on the front-end.

Using Angular with Rails is definitely a Good Thing(TM), but you really need a large enough project to justify, something both front- and back-end heavy. My current project is large enough to benefit from both, but unfortunately, I chose jQuery and Sinatra. Feeling the pain, for sure.