No need to send your users off to get embed code, the snippet of text needed to include videos and other rich media in a web page. All you need is the original URL to the content and Embed.ly returns the HTML you need, along with plenty of other useful meta-data. And it supports an impressive list of over 100 sites.
You can now use the YouTube API to access and create captions for your videos. That means you could let your site visitors refine the transcript to videos you own, or create their own versions of the caption.