You'll find a lot of love for Pocket Casts for good reason. The interface is slick, things are pretty well laid out, and the instant check for new episodes is awesome. It used to be the app used, and would be the one I still use if they didn't change how they now manage the queued up 'current' playlist. You used to be able to see all unread shows, click on one and it would play that unread queue starting at that show. Now you have to manage that manually. It also has some difficulty handling certain special situations (auto delete listened to podcasts except from this series where it should never delete. The wording on the screens makes you think you can do this but you can't.)

I've tried about a dozen apps and currently use the mostly inferior, but very flexible Doggcatcher because when you listen to as many podcasts as I do, at 2.5x speed, the manual queue management is unfortunate.