Well, it's a good thing I double-checked! My webhosting company specifically forbids streaming media, which includes hosting podcasts. So I have to find a solution for that before we can actually launch. I've looked at Libsyn and Podbean, I'm also going to take a look at Amazon's cloud services.
Anyone have suggestions for other options?
EDIT: Okay! Solution found, at least for the time being. Thanks, all!