Based on your requirement you really need to use Azure Storage for your content. Making your Azure Storage a CDN endpoint, is a decision content owner make based on how the content will be consume. As you are trying to store content for podcast, you sure can take advantage of CDN due to the nature of podcast as public service. So Having a Azure CDN service would be the best for you.
Before you decided to choose Windows Azure Media Service I would suggest to take a look here to learn how it works technically and weather you really need all of this. Windows Azure Media Service is end to end work flow for media content providers to encode, protect, distribute, stream to multiple devices. It may be something very big for your project and honestly not needed.
ポッドキャストユーザーにオーディオコンテンツを提供しようとしているだけなので、エンコードされたコンテンツをAzure Storageにアップロードしてから、CDNを介してユーザーに配布するのが最適です。それを圧縮する必要がある場合は、それを行うためにWebRoleが必要になる場合があります。これらの特定の分野のいずれかのコンテンツが必要な場合は、提案してください。私たちがお手伝いします。