Where to actually host your podcast is a huge question and one that needs considerable thought before you make up your mind. Questions that you will need to ask yourself include how big are my files, what is my Internet connection like, can I upload via FTP, and how much money am I prepared to spend.
Many people start up their podcast broadcasts for next to nothing, using free webspace that comes from their service provider. However, it is essential that things are reliable, as constant downtime is no fun for anyone - podcast makers and listeners alike.
Simply doing a search in Google for 'podcast hosting' is a good place to start with, and you will immediately find yourself with a variety of choices, such as the following recommended web hosts:
It is worth noting that many podcast websites are just simply directories. Therefore, they will not actually host your episodes as such, only link to them and help you reach your listeners. The giant that is iTunes falls into this category, and one of the numerous important factors in getting your podcast accepted into the iTunes library is that it is hosted in a sensible place.
Traffic Analysis Tools
Feedburner, PodTrac or Podbean all provide useful analysis tools that will help you make sense of both your website traffic and your podcast downloads.