Podcasts Questions

Hi, I know next to nothing about podcasts and I'm coming to you for a crash course.

I've decided to stop listening to so much music and try and educate myself or at least broaden my horizons through culture, etc.

I have an hour of driving a day to listen to stuff as well as pretty much all day at my job (6 hour shifts - however, I wouldn't be able to access iTunes or my iPhone to listen to them, I'd have to do so through a web browser if this is possible. My main concern in the commute, I can listen to other things at work like KhanAcademy, etc.)

Should I use the stock podcast app or is there an agreed upon podcast app?
How does one discover podcasts?
How do you add podcasts? Do you stream them (data usage problems?) or sync them like songs?
Does it cost money?

What are some recommended podcasts?

This may be the wrong place to ask this since my interests are more than simply Apple; however, I'm an Apple fan and tech enthusiast.
Other interests:
Finances, Scary Stories, Interesting History, etc.

I appreciate any and all responses - I tried to first search the forum for related posts but it's not the easiest thing to search as it's not indexed on Google.

Thanks again!