Best Python Web Framework for my API Server Needs
I agree with Anthony, you should look at Web2Py. It is very easy to get started, very low learning cure and easy to deploy on many systems including Linux, Windows and Amazon.
So far I have found nothing that Web2Py can not do. But more importantly it does things how you would think they should be done, so if you are not sure, very often a guess is good enough and it just works. If you do get stuck, it has by far the best and most up to date documentation for any Python Web Framework.
Even with all it's great features, easy use and up to date documentation, you will also find that the web2py user group on Google, is like having a paid for help desk staffed 24 hours a day. Most questions are answered with a couple minutes and Massimo (The original creator of Web2Py) goes out of his way not only to help, but to implement new ideas, suggestions and bug fixes within days of them being raised in the group.
I am working on developing two systems:  

A system that will constantly retrieve economic data from a 3rd party data feed and push it into a MySQL DB (using sqlalchemy)  
A server that will allow anyone to query the data in the db over a JSON AJAX API (similar to Yelp or Yahoo API for example)  

I have two main questions:  

Which Python framework should I use in 2)? Pyramid is my first choice, but if you strongly suggest against it or in favor of something else like Django or Pylons I am definitely wiling to consider it.  
Should I develop the two system separately? Or should 1) be a part of 2), running within the framework (using crontab or celery for example)?