If you're planning to launch a podcast, the first step to getting it on iTunes and Stitcher is to host it on a dedicated platform. While you might think that the cheapest solution of just hosting it on your own domain is the best route to go, remember that you'll need to ensure every listen or download of each episode is something your hosting provider can handle. In the end, it's usually best to leave it to the pros and invest in dedicated podcast hosting.
There are now dozens of hosting services for podcasts and vidcasts, but which one is best for you? Here are the top 3 (in my opinion) along with their pros and cons:
SoundCloud was the first to introduce easy sharing of music and podcast on a streaming platform. They offer a variety of plans and even have a free monthly plan to help get you started. And while their stat features are pretty good, the biggest thing SoundCloud has going against it is the lack of ability to schedule releases ahead of time, which means you'd have to be there uploading a new episode the same time every week. Hopefully they'll consider changing that soon, but if you're just getting started and want to dip your toes in before fully committing, they're probably the best platform to use. (Pro Tip: Check out this article by buyscplays about the best ways to utilize SoundCloud effectively)
Libsyn is the service I use for my own podcast. While they start off fairly cheap at $5/month, if you plan to have a weekly show and take on sponsors later on you're going to want detailed stats, which means bumping up to $15/month. They've recently introduced automated YouTube integration, which is amazing, as the more ways to hear your podcast the better. My main complaint with them is the interface, as it's a little rough and their integration with Wordpress sites is lacking.
I found out about PodBean thanks to Pat Flynn's side mention of it on one of his podcasts. PodBean seems to be siphoning off a lot of Libsyn's business thanks to their competitive pricing and ability to host vidcasts (video podcasts) and podcasts under one plan. From reviews on reddit, they seem to have a few kinks to work out, but are becoming a big contender for those who are considering doing more than just 1 podcast.
Whatever platform you decide to go with, remember that the biggest thing to your success is maintaining consistency and targeting your ideal audience with content they're looking for. Once you have your avatar figured out, start researching which of these 3 platforms is best for you, and you'll be sure to know your content is secure and isn't stripping away resources from your website.