I would probably say you purchase a vps or dedicated server then you can manage everything yourself and not have to worry about your disk space or bandwidth (as long as you have enough allocated to your vps/dedicated server to begin with) but i would recommend host gator for there servers there a good hosting company.
I don't have experience with either host, but I have seen good reports on both. What you have are two very different recommendations.
Hostgator has recommended a shared plan that they think will work for you, and it's an economical option. Take a look at their TOS, section 2, to make sure your video content is acceptable. They don't allow things like photo upload sites (such as PhotoBucket). If you have a question about your content and if it fits in, ask them specifically about it.
Knownhost has recommended what I would call a premium option, and it will give you the maximum amount of flexibility and freedom. To know which one of the virtual private servers (VPS) you can use, we'll need to know more about the applications you are running on the site. Is it a forum such as phpBB or vBulletin? Is it a Wordpress, Joomla or Drupal site? The reason I ask is that you are probably going to need at least their VPS2 with 768MB of RAM for those applications (and 1024MB would be better). That puts you in the $35 to $45 range. If that's a reasonable monthly cost for you, it would be great. But its three times the cost of the shared account. If it was me, and it was a non-profit or non-money making site, I would go with the shared account.
Im happy to go to $20.00 a month for a VPS, but there are so many I wouldnt know where to begin.
For a Wordpress site on a VPS, I would recommend at least 512MB of RAM as a minimum. There are folks who tweak the settings and get Wordpress to run in a smaller environment, but I think its cutting it close. Knownhost has a really good reputation, but I don't think their $25 VPS with 192MB of RAM would work well for Wordpress.
There is a huge price difference between "fully managed" and "unmanaged" or "basic management" VPS. Knownhost is a fully managed VPS and if you were to go with their $35 or $40 a month plan, you would be happy. Add $5 a month to have cPanel included if you need that. But it is a lot of money, at least double your budget.
An unmanaged VPS is not for the feint of heart or anyone who hasn't managed a linux server before. There are a lot of configuration items to be aware of related to server security, tweaking mySQL, keeping software updated, etc. The prices are much cheaper on unmanaged because you are doing all of that work. You can get a 512MB unmanaged VPS with 15 to 20 GB of disk space for $6 to $10 from some long-term hosting companies, like Burst.net. But they are unmanaged, so you have to learn how to manage the VPS.
You might find one of the smaller hosts who is willing to manage a small VPS like that for you within your budget. Especially if that's the only site you will be putting on the VPS (that makes it much easier to manage the server without a control panel like cPanel, or with one of the free control panels.) Or you could hire them to set it up for you if most of what you do will be from within Wordpress or via FTP. I've often thought there's a need for something in-between fully managed and un-managed, kind of a pay-more-for-setup then an hourly rate if you need more help.