Hi,
First create the page that you want to be accessible by members only. Lets say the page is named Foo and it has the url /foo.aspx and you set the view permissions on this page to the role "Authenticated Users"
Now the page exists but it is not in the menu if the user is not authenticated because the view roles filter for that.
Next create another page named Foo, check the box that says "Hide From Authenticated" Users in page settings and keep the view roles as "All Users". Set the Url for this page to the fully qualified url of the previously created page, ie http://yoursiteroot/foo.aspx
This should achieve your stated goal. There will be a link in the menu visiable to unauthenticated users but when the user clicks it he will be prompted to login and after login he will be redirected to the page. Now that he is logged in the previous page link dissappears because it has hide from authenticated and the previously hidden page appears because the user is signed in.
Hope it helps,
Joe