You may want to start out with free options like she mentioned just to prove the concept. But those will be slow and may have limited storage. You get what you pay for…
If you want to go into production, there are plenty of pay services out there for hosting servers and DBs. I don’t know them all, but I know there are places like AWS where you can get billed based on usage. Presumably if you are selling advertising (like the site you mentioned) you would go through the math of what a user would cost you and how much the advertising will make you. That’s just part of having a business model.