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There are a lot of different Backend Solutions and you should take what fits your websites purpose and also personal preference the best.
If Backend includes Hosting in your case then you basicly have the 2 big options:
a) A Server where you run it ex. via an Reverse Proxy (example: Digital Ocean)
b) A cloud computing Platform (example: AWS, Heroku, App Engine)
But you only need to host it that way if you actually run the app and retrieve dynamic updates on the page, new routes get added when you for example publish a new Post.
If that is not the case then a static hosting provider would be enough, there are 1000´s of them and they are pretty uncomplicated.
If you mean which Database to use, then it also comes down to preference, do you want a SQL Databse or a NoSQL Database like MongoDB? As a personal recommendation I would suggest you to use Firebase as your backend for your experimental app, the free plan is far than enough for testing purposes, you also have a smooth and easy to integrate Authentication System avaliable and you can also take quick advantage of things like Push Messages, Cloud Storage Buckets and more.
Note that Im not related to FB by any means and this is just a personal recommendation, but I feel like your Question is pretty opinion based so maybe be more specific about your goals or just comment down below if you got any more questions.