I'll also recommend PocketCasts on Android - it lets you do some nice things with custom playlists, etc. and there are a few features that you may not find immediately so play around. If you have multiple devices (e.g. phone and tablet) it syncs listened and position data between the devices, though it doesn't show on them which items have been downloaded on a different device.
When you're looking at the list of podcasts, you can long-hold to select (after selecting the first, taps select additional ones). Then you can tap the + icon at the top to add the selected podcasts to your "up next" list.
To manage the Up Next queue, start a podcast playing and get to the view for that episode (it'll be taking the full screen, not the popup of show notes). The icon at the top right that looks like a bulleted list is the one for managing the Up Next queue.
Finally, there isn't a good way to mark a podcast as "unheard" rather than partially played - the workaround is to open the show notes popup by tapping the episode, then tap the icon for marking as heard, then tap it again to mark as unheard.
When you're looking at the list of podcasts, you can long-hold to select (after selecting the first, taps select additional ones). Then you can tap the + icon at the top to add the selected podcasts to your "up next" list.
To manage the Up Next queue, start a podcast playing and get to the view for that episode (it'll be taking the full screen, not the popup of show notes). The icon at the top right that looks like a bulleted list is the one for managing the Up Next queue.
Finally, there isn't a good way to mark a podcast as "unheard" rather than partially played - the workaround is to open the show notes popup by tapping the episode, then tap the icon for marking as heard, then tap it again to mark as unheard.