From the description given, my impression is that you want an app that can make multimedia content on your local network accessible. If that's the end goal, a website is overkill.
Here's what I can write.
1. The app will list all the files on your local server in a nice UI( similar to netflix android app ) and automatically get all the thumbnails and related metadata for the file( movie or a tv series ).
2. Save status of all files( like last watched till XX::YY, already watched, yet to watch, etc... ) and manage your media properly.
3. Account management in the app which can handle multiple users and their own saved status. Allowing of pausing on one device and then continuing on another device.
I'd be happy to talk if you want something else added. I'm a student and am new to this website, hence I don't have any reviews yet, but I can say I'm a very good programmer.