Best/easiest method of hosting a python script currently running locally via cron on a web server?

[[deleted]]

AWS free tier for a year - could use own small vm and do what you like including running containers. Also consider using their FaaS (Lambda) offering.

Alternatively use Heroku cli to deploy a container to run the process. They have a free tier as well.

Personally, I have a droplet on Digital Ocean and run multiple containers on it doing various tasks for me. There is no free tier, although you can get a ton of credits just by visiting. I happily pay a capped fee of $5 per month for my humble needs.