Python and Flask on Heroku. What you're describing is almost the "tutorial" web app (look up Grinberg's book on Flask). Heroku is a nice platform to work on that takes a lot of the complexity out of cloud hosting. Flask lets you do almost all the coding yourself, but it has add-ons available to take care of whatever you don't want to do.

Heroku gives you a PostgreSQL database with one click, but you could easily integrate a MongoDB database if you wanted to try NoSQL. In Mongo, you'd actually store and retrieve your data in JSON, so it's even easier than writing SQL.