The default behaviour of mysite.com/post-type/
and mysite.com/post-type/post-name/
is what you want it to be, so you don’t need to do anything special there.
To have mysite.com/post-type/taxonomy/
as the URL for the taxonomy archive, all you need to do is use 'post-type/taxonomy'
as the rewrite => slug
argument when registering the taxonomy.