1. For starters, anyone who has been around any form of serious web hosting environment will quickly tell you that there is NO such thing as unlimited hosting. There are no unlimited hard drives and there are no unlimited bandwidth connections. At some point there is a limit. Unlimited hosts may be getting better with the proliferation of massive hard drives and fast connections but there will always be a limit somewhere.
These shops tend to target smaller setups who have very small resource footprints and that is fine, but as soon as the resources grow to some, often unwritten, soft limitation you will have problems. This also tends to lead to a lot of overselling. Again if the resources are there it is not a big deal, until hundreds of accounts on the same server start trying to use the same chunk of unlimited bandwidth.
If you value the quality of your service and intend to have your site/service grow to a sizable level then do yourself a favor and steer clear of the allure of unlimited hosting. If you're just using it to get your feet wet and get off the ground it could be a cheap way to get started. You get what you pay for.
2. Video processing is going to require memory and processor resources. These are probably the most expensive and limited resources in a server. If your site sees any kind of steady traffic, you will probably quickly outgrow a shared environment and even possibly a VPS solution. Plan accordingly.
3. I'd suggest you check out http://www.webhostingtalk.com/ It is a great resource and there are a huge number of hosts who actively participate.