How to host selenium Python script with file system access?
I suggest you to look at AWS (since is the only platform I've been working with).
With it's free acount you can use an EC2, where you can store your script and dependencies, and your output can be written in an S3 instance (free for 30GB if I remeber well).
As you are going to use Selenium, you will need a GUI for your system, so your choices are a Windows machine for EC2 or Linux (does not came with a graphical environment by default). It is not difficult to install a GUI on Linux machines and configure to acces by RDP, but I suggest to use instead a simulated graphical environment such as XVFB. I used it and is as simple as launching your script with xvfb run first. That way you are saving some processor load for your machine.
I hope it helps,
Regards.
I've recently been working on a little project and I want to host it on the cloud so it can run all the time, rather than constantly on my local machine.  However I'm kind of stumped when it comes to choosing a hosting solution, and I was wondering if you guys could give me some advice.
Some details about the project:

It's a Python script, not a web app, and should be running constantly (actions are scheduled once per day)
It uses a few fairly large external dependencies, namely Selenium and Chromedriver, which requires binaries to be installed on the machine and grabbable (not sure if that's a word) by path from the script
It uses a few static files (mp3) as assets, which need to be stored on a file system somehow and grabbed by the script
It writes video files to the local filesystem

Do you guys have any recommendations for hosting solutions which satisfy these details? I've tried with Heroku, which satisfies details 1-2, but since Heroku has like a weird "ephemeral file system" I can't grab the static files nor write video files to the file system.  
Thanks for the help!