How can I create a website that can hold a high volume of video content?
You are right; costs to develop and operate these kinds of sites are high. While I can't recommend web developers specifically, I would recommend taking a look at some of the sites that offer video content and try to determine who designed their site--you might even want to call or email the website owner and ask. You might get a glowing recommendation.
And, while you've got them on the line, you might want to ask them about typical startup costs associated with operating a video website. You might also reach out to a company called Media Temple. This is a hosting company for many web 2.0 websites and they might be able to point you in the right direction.
Make it happen,