Rule of thumb - always try and land the .com. In your case you really do need the .com and here is why - You're doing a video site, sounds like a tube site. One that should get repeat visitors, often, as the goal. If you develop it out with the .tv you're going to be giving the .com owner of the same term quite a bit of traffic, 10-20% of your type-in/returning visitors. It will only cause confusion and hinder your growth. Think about it - someone stumbles upon your tube site and tells his friend, do you think his friend is going to type in Domain .tv or Domain .com?
As for using others videos on your site. Throw up a DMCA and then make damn sure you're not the one as far as logs are concerned uploading the content. Remember your "members" are.