Bridging a Python back-end and JavaScript front-end
Flask is easy to get up and running and is Python based.  It works well with REST APIs and data sent by JSON (or JSON API).
This is one solution with which I have some experience and which seems to work well and is not hard to get up and running (and natural to work with Python).  I can't tell you whether it is the best solution for your needs, but it should work.
If you are overwhelmed and don't know where to start, you can pick one of the options and google search for a tutorial.  With a decent tutorial, you should have an example up and running by the end of the tutorial, and then you will know if you are comfortable working with it and have an idea whether it will meet your needs.
Then you could do a proof-of-concept; make a small app that just handles one small part (the one you are most concerned about handling, perhaps) and write something which will do it.
By then, you can be pretty sure you have a good tool for the purpose (unless you were convinced otherwise by the proof-of-concept -- in which case, try again with another option :-))
I'm currently working on a project that involves parsing through a user-supplied file, doing computations with that data, and visualizing the results using graphing utilities. Right now, I'm stuck with using Python as the back-end because it has scientific libraries unavailable in JavaScript, but I want to move the entire tool to a web server, where I can do much slicker visualizations using D3.js.
The workflow would be something like: obtain the file contents from the browser, execute the Python script with the contents, return jsonified objects of computed values, and plot those objects using D3. I already have the back-end and front-end working by themselves, but want to know: How can I go about bridging the two? From what I've gathered, I need to do something along the lines of launching a server, sending AJAX requests to the server, and retrieving data from the server. But with the number of frameworks out there (Flask, cgi, apache, websockets, etc.), I'm not really sure where to start. This will likely only be a very simple web app with just a file submit page and a data visualization page. Any help is appreciated!