I'll give a shout to Pocket Casts which I think is a couple of quid. It's possible the free options have got better, but I went through a bunch of them and found them all annoying for one reason or another before giving Pocket Casts a go and it does everything really well: syncs across different devices, nice UI, podcast search works really well, discover page is useful for when I want something new - I've just found it pretty much niggle free and given the amount of use I've got out of it I don't regret (or think about) having paid for it at all.
I'll give a shout to Pocket Casts which I think is a couple of quid. It's possible the free options have got better, but I went through a bunch of them and found them all annoying for one reason or another before giving Pocket Casts a go and it does everything really well: syncs across different devices, nice UI, podcast search works really well, discover page is useful for when I want something new - I've just found it pretty much niggle free and given the amount of use I've got out of it I don't regret (or think about) having paid for it at all.