Where you host will depend on lots of things like who creates and owns the content, who consumes it, what budget you have, etc. I have a few of channels I work on, two of them I host on IIS servers. One is in my home and just streams "home movies" to the Roku's in my home. Another is used in an office environment and is used to stream company meetings (both live and past recordings) to conference rooms all over the campus. So for both of these it was all intranet use. Most of it I would do quite differently if it was for extranet use as well. A third channel I work on uses Windows Azure to store the videos (the videos are about 30 seconds each) and those are streamed to the end users. But the extranet one I would design differently if it wasn't just 3 people who manage all the content.
The questions below may help you as they can help you determine storage, bandwidth, security, etc.
Who is creating your content?
Who owns your content?
What kind of security is required for reading and writing content?
How much content do you have (MB/GB/TB)?
Where are your media consumers?
How frequently will it be accessed?