I would like to create a blogging website for other people, based on Wordpress. They could sing up, select their subdomain name (it would be good if they would be able to add their fully qualified domain name also), and start adding posts.

It would be good if I could add any of the Wordpress plugins / themes etc. Is something like this possible? I think it should be, but I am not sure if something like this is readily available on the Net. I was looking at Buddy Press, but I am not sure if this is exactly what I need (it is more like a social blogging software, like Tumblr, and not regular blogging site).

What would be the best way to do it?

Thank you.