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...).
You could deploy on cloud servers such as Amazon EC2, Rackspace cloud or Liquidweb StormOnDemand.
Choose a framework that will server you well such as Symfony2 (PHP).
Make sure your code is source controlled (git).
Make sure you have deployment tools to keep your production site up to date (capistrano/capifony).
If you want anything to scale, you can't use WordPress. Which is probably why you said not using WordPress...I imagine you tried or were told. You can count out many other CMS' as well to be frank. Especially if they use MySQL. You'll run into absolutely too many bottlenecks that can only be solved by pouring money on the fire in hopes to extinguish it.
You'll need something custom built using a rapid application development framework. Language? Up to you really, take your pick. For PHP you have The Lithium Framework (not to be confused with Lithium period), Symony2, and a few others. For Node.js you have Sails and Express.
Use these with a database like MongoDB, Couchbase, etc. Anything NoSQL because you'll likely want high read performance and a schemaless database is just awesome for build speed (again taking into consideration your cost requirements).
That should take care of your CMS needs and using technology like listed above (though not limited to what I listed) will allow your application/platform to not only be built fast, but also scale to handle a lot of traffic. Further, it makes maintenance easy. Don't forget that once you build an app or website, that you need to maintain it. It's rarely ever a "done" thing. Various bugs, new features, tweaks, etc. When your codebase is very well organized and fast to work with, you win.
I'd also think about utilizing Amazon Web Services...They have a new one that does video transcoding on demand. You also will want to host the actual video files and I think Amazon provides the cheapest way to do that too.
That's how I'd build a video platform to be honest. Everything for development speed and mass read performance. Uploading is a bear and you will need powerful servers for video, but the more you can offload onto "cloud" services, the better off you'll be. The faster you can build and maintain your code, the less money you'll be spending.
Of course it should be noted that having some guy (or girl) install WordPress for you will, initially, be cheaper than a custom build...But over time your custom solution will pay off.