React with a simple router and perhaps some help with your models (Flux or Backbone) might be enough for your needs. Any user behavior that requires new data could be an ajax call that passes back the entire state of the current 'page', which could then replace the state of top-level component (since you want most of your state to reside there anyways). React takes over from there. You'd be relying mostly on your server-side framework for the logic.

You could then incrementally add logic client-side to improve performance, if that's necessary (if the state object becomes too large, for example).