If the materials I am assembling are all public domain or out of print, do I still need to go through the permissions process?

If you can determine the content is public domain, you do not need to go through the permissions process. In the case of out of print materials, you are still required to confirm with the rights holder if the material is truly out of print before using that material. Notification from the publisher that the material is out of print is the only acceptable verification.