you could break it down into two components.
1) The primary hosting provider (no less than a VPS).
2) The media provider, a host dedicated solely to hosting streaming media.
While I don't have any good suggestions off the top of my head except for part #1 (I use KnownHost personally for my VPSes but I don't run a streaming media site), I will say that most of the top dogs use at the very least the above suggestion separating the actual media hosting from the primary hosting.