Podcast placement strategy

Hi, I’m getting ready to launch my podcast. I’ve had a blog and weekly newsletter for several years.
Where is the best place to post the new podcast episodes on my website: in the existing blog as blog posts with audio files, or in a separate ‘podcast’ page? (I know many people will just download in their podcast player, but wondering what’s best practice in terms of SEO, UX, etc. on my site.)