Building a private API to connect with mobile app?

I'm attempting to build a private API to connect to my mobile app. One use would be to make a call with a string parameter, have the api run the string through several nlp python scripts, and return back some json. What would be a good place to start in terms of api services and resources?

So far I've heard that I can use Django Rest Framework for this, but I wanted to make sure to ask people with more experience. Also what's the best place to host it, including the scripts (my hosting with namecheap, amazon s3, etc)