Grover Podcast is a free tool for finding, playing and listening to podcasts.
The program opens in an empty "My Podcasts" area, but entering something in the (iTunes API-integrated) Search box should give you plenty of hits from the "Podcast Store".
If not, browse various categories (Arts, Business, Comedy, Sports, more), subscribe to whatever you like and it'll be added to "My Podcasts" for easier access later.
Or you could just import an OPML file, if you've already got a podcast list elsewhere.
Select a podcast and it's ready to play immediately. Normally this will be locally, but there's also a "cast to device" button to stream it elsewhere.
System notifications then let you know when a new podcast is available. Grover Podcast can download these automatically, and even remove them automatically once they've been played-- all you have to do is listen.
A stylish podcast manager, easy to use and with all the core features you need.