I'd like to create a website creation tool that allows the user to publish their website on the web. I don't want to do the hosting side of it, so I'm looking for a web host that offers an API so that my app can programmatically create user accounts, upload files, etc.
Note that FTP isn't enough because I want the user to be able to do everything from within my app, including creating a new website. Also, I prefer to make simple HTTP requests-- just standard web API stuff.
What options are available?