I have three great, free options for you if you're looking for a free way to host your podcast. The first is a podcasting service called Anchor.fm, the second is a podcasting service called Sounder, and third, there's an option of uploading and hosting your files from Archive.org.
Several years ago I recommended here hosting sermon audio in the cloud for free at SermonCloud.com. They no longer offer from sermon audio hosting but there are other options now.
Two services I recommend these days are Achor.fm and Archive.org.
As a web developer especially interested in helping churches for many years now I'm often asked “how do I add audio to our church website?”