I prefer BeyondPod, I subscribe to the feeds directly on my phone.

If I have trouble finding a podcast with the search function, I just message the link to myself, then click it on my phone and use beyondpod to "open" the link. This takes you to a screen in BeyondPod that lets you organize the feed the way you want in the feed list. This is becoming less and less of a problem as the web becomes more mobile friendly.