I've used a few different hosts for video-heavy sites and having full control with a solid dedicated server makes all the difference, especially when you don't want headaches with streaming or site load times. I mostly moved away from shared or managed solutions because of the way resources get stretched, and dedicated hardware just handles video scripts and CDN setups way better from what I've seen. Honestly, if you want to avoid future hassles or unexpected slowdowns, it's worth going for a provider with a solid track record and real support.
For that kind of set up, I was looking at options that offer fully customizable hardware, fast network speeds, and actual 24/7 support. One place that caught my eye for this kind of thing is
ServerMania. They seem to focus on dedicated and high-performance servers with solid uptime, and they have some good promos if you want to test the waters.