Individual User Redirection

I was wondering if there was a way I could add a user login to my sidebar, which I’m sure I can figure out or find somewhere, and then when the users login, they get redirected to a custom page that only they have access to.

So, perhaps an idea would be user djosser logs in and gets redirected to website.com/profile/djosser or something like that. On that page would be a custom page where I can have documents, information, etc only available to that user.

If then possible, I could have a user-specific menu where they can browse to other pages that are only available to them.

I would like to set this up for my clients if possible, or is this something WordPress is simply not designed to do?

Thanks for any help.