I use buzzsprout, and you can post links to your blog; they do what they do well. Keep your podcast hosting separately. Buzzsprout provides all the info you need. There are others out there. The only thing to remember is it takes a lot of work and commitment, and you are looking at a long term growth strategy to get it to 3k downloads, then 5k, then the magic 10k for revenue. But if you are just using it for PR, then that a different strategy. Good luck. Niche is king on podcasting as well.

I heard good reviews about Anchor.fm and Buzzsprout. They have tutorials on how you can add podcasts to your blog.
I will also check what Carson has suggested.

Hey Jenni,

Providing video or audio (podcasts) content on your website is best with a dedicated video/audio streaming service. One service that we use at Wealthy Affiliate is called Wistia and we can't say enough good things about it. Have a read of the following link about their podcasting services:

https://wistia.com/product/podcasting

There are many companies out there that make it easy to add podcasts and video to your website, Wistia is just one worth mentioning.

The benefit to using a streaming service is that their player will be very easy to copy/paste (embed) on your site, plus it'll be very compatible with all browsers and mobile devices. Your audience will also experience far smoother and faster streaming vs trying to upload directly to your website. Website hosting servers are far different than video streaming servers, so the experience for your audience will be far less ideal than using a service like Wistia!

Hope this helps,

Carson