Create a page selector using taxonomies

This is a very broad question so I am going to offer an outline.

  1. Use get_terms to create your first select box.
    1. This would be done in PHP.
  2. For the second box you will need to use Javascript.
    1. Using Javascript, watch the first select box for change
    2. When something changes, grab the ID of the selected term and request
      the pages assigned to that term using the AJAX API.

      1. In the AJAX callback, you’d have a pretty standard WP_Query to
        grab the posts.
  3. Once both boxes are populated, your Javascript can insert the button
    into the DOM

It should not be very complicated but it is a fair bit of code. Try to get started and [edit] your question with more specific problems if you need to.

Be aware, that pure Javascript issues/questions are off-topic here per the faq. Obviously, though related to Javascript, the use of the AJAX API would not be off-topic, as that is a WordPress specific API.