I love Wordpress, Magento, SEO, SEA, Analytics, Affiliate marketing, etc... i made more than 300 websites and i work for hudge company to improve their online activies.
As an affiliate marketer i need to track all the click on my links across all the websites... i investigated in Goo.gl and Bit.ly solutions but i wanted a hosted solution. I found Yourls an open source shortener and Prosper202. I use Yourls with a Google Analytics plugin on my own domain name www.jeclic.com and i can see all the click as page view in GA, i have interesting detailed reports :)
I suggest like everyone to use Wordpress, perfect for beginner ! You'll find several plugins to make a video streaming website (ex: https://wordpress.org/plugins/stream-video-player/)... You can use the tools they mentionned above to look for the CMS and plugins used. Tight budget + beginner = Wordpress by far ;)