I had a listener ask me for my opinion on using Free Media hosts such as Podbean.com While I understand that some times there is no budget and free is your only option. For the record, podbean has some nice features and they make things easy. I also know people who have grown in and out of podbean (and moving is no fun). If free is your only option then I would recommend www.mevio.com (although they may insert ads into your show, and you won't get paid. However, you are getting free bandwidth, storage, and stats).
I look at it like moving into a house. You can move into a starter house with one bedroom, etc. Then later if your family grows you can move into a bigger house. If you had the chance, and could afford it, wouldn't rather skip step one? After all moving all your stuff is no fun.
Likewise when you set up a podcast on a free account, in some cases they set up an RSS feed for you (bad) and set up your iTunes listing for you (very bad), and then you are set with limitations (storage, etc). In other words, you get what you pay for.
If you can afford $10 a month for hosting your website (I use Hostgator – affiliate link), and $12 a month at Libsyn.com then that would be the route I would go. In some cases I've seen people host both their website and their media on Host Gator. This works, but you will have to struggle to get some stats, and if you get really popular you will be asked to move your media.
The other thing to consider is many free sites go out of business (forcing you to move again). If you can avoid it, I would. People go in with a negative attitude. They say, “What if nobody listens?” To this I ask, “But what if they do?! – you will want a more powerful site with more features.”
Plan to be successful. You'll be surprised how quickly you can grow an audience with a little promotion.