I have used this sermon plugin on a lot of church websites. I've actually used it on some non-church sites that needed an organized video library. It is hands down my favorite to use right out of the box.
- Looks the best right 'out of the box' with no configuration.
- Doesn't need theme integration to look awesome.
- Added to whatever page via a simple shortcode.
- Now has modules with Beaver Builder and Divi.
- Lifetime license is hard to beat.
- Exploring the library is easy to users.
You can read a bit about why I love Series Engine on this post.
This sermon plugin works great with supported themes. You can also use it with Beaver Themer, but to date I haven't personally toyed with that combo. This plugin also handles events, locations/campuses, and staff/team.
Price: Free (most compatible themes cost)
Having a sermon plugin is just the tip of the iceberg. It's debatable these days, but I still maintain that your website (unless you're on some megachurch enterprise plan) is not the best place to host your audio files . I recommend offloading to one of these guys instead.
AmazonS3 just hosts the files.
Soundcloud, Libsyn, Buzzsprout and AudioPod are my recommend podcasting solutions. They host your files and push out your podcasts. For the sermon area, just drop your audio link into your sermon plugin to display the audio on your site.
For video, just upload it to YouTube or Vimeo and use the relevant links to add to your sermon player. No reason at all to have that on your site.