This is indeed a good question because it really hits on two slightly different areas.
Who hosts the content? YouTube, Vimeo, Wistia, Vzaar, Amazon Web Services… You?
Where is the content hosted? The UK, USA or elsewhere?
In order to have the least amount of pressure on your server it’s best to have your online video content hosted by a professional hosting company such as those listed above. Of course, there are many more, but these will serve as a good example for now.
The reason it’s best is that you will not be storing the actual video itself, which could well be a very large file. Once you’ve multiplied this by the number of videos and therefore files, you end up with a very big number and the risk of quite a drain on your server. So, the preferred way is to use a professional video host who will provide you with a link to a video stored on their server.
The question you have to ask is that when you access that content what else do you access at the same time. For example, if you access content from YouTube or Vimeo you’ll also get access to similar content and all of the services and content of those suppliers. So, your question has to be: “Do I really want my staff on YouTube during the working day?” In fact, many companies simply deny access to products such as YouTube for that very reason.
What you need to look for is a video host that will deliver your video content and only your video without the risk associated with the likes of YouTube. Hosts to consider would be Amazon Web Services and Wistia (which Mi Crow uses) to name but a few. Both provide excellent services continually developing their products to make your viewing the best and most functional it can be.
Where your videos are hosted is a completely different ball game entirely.
What’s important is your location as you could find that you’re in the UK with your videos being served from the USA and whilst the time difference may well work in your favour there’s likely to be a time when everything slows down due to the demands on the servers in the USA. However, a lot of businesses now want content and data to be stored within their geography for reasons around data protection and performance (amongst others).
Many providers, irrespective of their locations deliver video content from local servers close to your location and consequently deliver continual high performance.
So, whilst hosting may not be the most prominent question for you it is something that could be significant in your overall solution.