I'm sorry if my question is too elementary. I have some python code, which makes the machine act as a transparent proxy server using "twisted" library. Basically I want my own transparent proxy OUTSIDE my internal network and since I want to be able to monitor traffic, I need to have my own server. So I need a machine that runs my script 24/7 and listens for http connections. What kind of server/host do I need? Any host provider suggestions?
Go for Amazon Ec2 instance, Ubantu server. If your process is not much memory consuming , you can go with Micro instance(617 Mb ram, 8 Gb HD) which is free for first year. Or you could go with small instance (1.7 GB ram and 8Gb HD), which might cost you little more. 
For setting up the python code to run 24/7 , you can create a daemon process in the instance. You can also put the twisted library/ any other library in it. Should not take much time if you have worked with Amazon AWS.
Web server to run python code