So, let me tell you what I did starting out, and why that's eventually a bad idea.  Then I'll tell you what to do. 

So, when I was still doing internet radio, and had a button you press to 'tune in', what I had going on back in the late 90s/early 2000s was mp3 files directly on my webhost.  I had a table on the back end that would figure out what time it was where you were, and serve you the mp3 that I had designated for that time slot.  I had it split up in 15 minute segments to make up a 24 hour day.  I had 6 'shows' that you could hear over a 24 hour period.  This was prior to anything about the web we know today. 

Back then, it was easier to just place the files on your server.  These days, I wouldn't do that.  Especially if you are lucky enough to hit a Trending section.  Most webhosts out there say that they give you unlimited bandwidth, but if you get popular enough to disproportionately affect the bandwidth on a server, you're going to find that the provider isn't going to be happy with you.  Unlimited doesn't always mean unlimited.  

When it comes to podcasting, I would use a service like Libsyn or Blubrry, that are specifically designed to deliver your podcast files quickly, and at scale.  I've used Libsyn for years, and I have no complaints.  One particular episode I released where I explained the Obamacare bill in plain language was downloaded over 10,000 times within 48 hours.  It was a rather large file compared to other podcasts I've done.  It was a 2 hour show, and over 150mb.  If I had stored that locally on my Webhost server--which I no longer use--I'm convinced it would have crashed the server not only affecting me, but all the other websites occupying the same server I did.  Podcast delivery networks like Libsyn and Blubrry have redundancies in place for this eventuality.  They are extremely affordable, and in the case of Blubrry you have the opportunity to get ad placement, which may help defray the cost. 

So, to recap, never put your podcast on your own server.  Pay a little bit of money, and use a tried and true delivery network.  Remember, they won't continue to listen to your podcast if they can't download your podcast. 

Blog, Q An A-HoleRoley