I just recently wrapped up a project that was similar to what it sounds like you are looking for: a web application that adapts the user experience to the type of device being used, desktop or mobile.
Part of the answer depends on if you envision your application being distributed to mobile platforms only on the web or if you plan on releasing mobile applications available in the App Store or Google Play.
For an application that is web-only, the key phrase is "responsive design." An ideal front-end architecture would be AngularJS + Bootstrap.
For an application that may also be deployed as a mobile app sold or offered in an app store, the AngularJS + Bootstrap combination mentioned above would work well with PhoneGap as a container. I prefer Sencha Touch for HTML5-based mobile apps as the user experience is excellent, with the downside that you have to write separate applications for mobile and web as it is not a responsive design framework.
For the back end, it's really up to what you are comfortable with, how conservative or bleeding edge you want to be, and how you see the application growing over time. The important part is that the back end is completely uncoupled from the UI, providing data via services that the UI can consume as opposed to generating HTML.
Feel free to contact me if I can help more!