What hosting services do you recommend for podcasts?

My guess would be Twitter or a personal blog or networking with folks would be the best ways to promote your podcast. Twitter is where I've discovered most of the podcasts I listen to. I don't know much about hosting providers for podcasts in particular, but I found the follow resources that may help.

http://www.labnol.org/internet/host-podcasts-on-google-drive/28227/

http://www.podcastinghacks.com/how-to-create-your-own-podcast/

https://garage.godaddy.com/webpro/wordpress/how-to-start-a-podcast-with-wordpress/

https://tryca.st/?ref=producthunt

https://www.reddit.com/r/podcasts/comments/3o8g0h/podcast_hosts_squarespace_vs_libsyn_vs_podbean/

https://growthedream.com/host-podcast-files-amazon-s3/

Also check out this podcast episode from CodePen that specifically talks about Podcasting. They have a great list of resources too so I think listening to this and going through that list will be the best help for you. http://blog.codepen.io/2015/06/11/043-podcasting/

Shop Talk Show also occasionally talks about how they do their podcast but I'm not sure what the specific episodes are. http://shoptalkshow.com/