Podcasts are mp3 files, so, if your player will play MP3s, you can hear them. iTunes will download them but not automatically transfer them to your player (if it is not an iPod). You find the folder it stores them in and copy the files to your player. (Hopefully, your player looks like a drive to your computer and you just use whatever file copying software that you usually use.)
From my experience, there are some qualities you would like to have in your player. Unfortunately, I don't know how you tell whether a player you are expecting to buy has these qualities.
Note that many podcasts are a 1/2 hour or more long. Can you expect to be able to listen for that length of time without interruption. If not, you need to be able to pause the player. All of them allow that (AFAIK) but for how long? Mine pauses for a minute and then shuts off. And loses its place. If I have noted where it was when it shut off, how do I get there? (There is a fast forward function, but not terribly fast.) So, it would be good to have: (1) Infinite Pause, (2) Set and Goto bookmarks. And long life batteries.
My cheapie also only tells me File 1, File 2, etc. A screen that gives a file name would be good.
Podcasts tend to be recorded at good quality, even though most are all voice. File sizes of 20MB or more are common. High capacity is good. I have taken to downsampling them to make them smaller.
-----Sims-----
hello all,
I am preparing to buy an mp3 player but i had a few questions first. I want to download podcast's from KCRW and NPR, etc. if i buy an mp3 player that is not an ipod, can i listen to podcasts? will i be able to use itunes?
thanks,
Aurash

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic