Looking for guidance on creating a private podcast.

As the title says, I'm looking at the logistics of a private podcast and what that would entail.

I am a Nurse Educator at our hospital, and we were toying with the idea of starting a short form podcast as a way to provide learning in a different format. Is there a way I could record/edit these audio sessions and then host them somewhere that only our employees could access?

The most inexpensive and simplest route would be preferable. We do not require fancy features and are not looking to monetize this in anyway.

Thanks in advance for any advice!