Creating public user profiles

I want to create a site where once you purchase the product I am selling, you are redirected to your profile page where you can edit your info. I want that user profile to be publicly available so anyone can visit it.

For example, John Doe makes a purchase on my site, after checkout he is redirected to an account creation page. John edits his user profile and the page is published. The url will be mydomain.com/profiles/johndoe for example. I want it that he can go back in, login to his profile make any changes he needs to and republish it. That profile is accessible to the public by going to this domain without login in.

Is this possible?