Microsoft Azure. For startups they give you a ton of stuff for free, and if you talk to someone there you can probably get even more. And when you're eventually ready to pay, you can just continue with them.
Google's cloud offering is also free or cheap, but it's unclear what the future of that is, and it's much more limiting.
If you don't want to be a member of any special programs, then design your system to be deployed directly to S3 so you can serve from there. That's cheap, and you get arbitrary scale built-in, and you can add "speed" to that by fronting with a CDN when you're ready to pay a little more.
In general, though, video-streaming is NOT FREE. You should design for the video-streaming part to be hosted by someone else -- YouTube, Vimeo, anything. That's a whole business in itself, and bandwidth is expensive until you're very large (and even then...).