Summary: I believe a MEAN Stack application would be the best solution for what I have in mind. If you think otherwise, please let me know!
Basically, the web app will match users based on the movies and TV shows they like, and if they have a certain % of titles in common with another user, you can chat with that person 1 on 1.
There are two main components to the project. The logic side (handling logins, the movie and TV selection, as well as calculating matches) and the chat side (connecting users, managing a list of contacts, etc).
Total estimated time for this project is 18-22 hours of work.
Please see the attached document for a detailed description of the project requirements.