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.