I came across a page on the codex today that showed me a way of creating admin pages that I didn’t know about before. This allows simple plugin settings page to be created that update themselves without any additional PHP.
By creating an admin page with the appropriate nonce, action, and page_options fields you create an options page that gives WordPress enough information to handle the form submission, save the options, and handle the redirect back to the same page again.
Before now I had been creating pages to do a lot of this manually.
You can read the full details about creating options pages on the codex.