Well it depends on how you are doing the streaming videos. Mostly people use a dedicated server for streaming videos, because running videos on shared hosting account probably cause some issues, but if your site have a low amount of traffic, then I am sure vps will work fine.
As you are going to use video files on your website, then at least you need to choose vps, and it's well affordable solution as well. But you need to pick vps package who has an adequate bandwidth.
A vps hosting environment will allow you to place the video files on your website in advanced downloading format. For a short length videos this will not be a problem, but if you are going to use lengthy videos like 15 to 20 minutes, then you may want to look for a dedicated hosting.