Need to install a Wordpress on demand, or use one independently with different databases

Hi, I was wondering, if it was possible, that I have a website, where someone can sign up, and instantly use a brand new Wordpress install on my server (installed in a directory that's named by the user, and able to login to the administration panel). I would need a "script" like that, that creates and sets up a Wordpress in seconds. One other option is, that there is a highly modified Wordpress install on the server, and after the user signs up, he can use this software with his user ID, but everybody would use the same WP PHP files, so there is no need to have a dozen WPs installed on the server, only one, which can serve many users (the users should be able to upload their own content, choose different templates, and all users should be able to access their website from a different domain/subdomain). My budget for the first option is max 250 USD, but for the second option it's higher. Please state if you can help me with the second one too, and for what money. Thanks!