Build a Server to Receive and Send User's Private Information
You don't need to create your own encrypted communication protocol. Just serve all traffic over https.
If you also wish to encrypt the data before storing it on a database you can encrypt it on arrival to the server.
Check out Express.js for the server, Passport.js for authentication and search for 256-bit encryption on npm. There are quite a few implementations.
I'm getting started out creating a website where users can store and get (on user request) private information they store on the server. Since the information is private, I would also like to provide 256 bit encryption. So, how should I go about it? Should I code the back end server stuff in node.js or Python, since I'm comfortable with both languages? How do I go about providing a secure server to the user? And if in the future, I would like to expand my service to mobile apps for Android and iOS, what would be the process?
Please try explaining in detail since that would be a great help :)