Another option would be to use an ad-free platform like Vimeo. Their basic plan gives you a 500 MB per week limit and there is no bandwidth limitation. They give you access to basic analytics and format your videos cross-platform compatibility.
If you are using videos for Video Sales Letters, or if you need advanced analytics, CTA buttons A/VB testing etc, it is better to go for a paid option like Wistia. You can take a test drive of their system before committing to a plan. Their free plan gives you 200 GB bandwidth and 25 video limit. The paid options will give you an unbranded player, analytics like heatmapping, engagement graphs etc. Integration with MailChimp, WordPress and other tools is a breeze.
This is an ideal way to set up commercial video hosting. Vimeo also offers a paid service called Vimeo Pro. using this service, you can restrict video to a certain audience. This is very useful if you run a membership site. You get unlimited bandwidth, priority upload and conversion and advanced analytics.
The biggest advantage of using a professional service is that streaming is faster through their CDN than a website hosting. So even a HD video can be streamed effortlessly and without worrying about escalating bandwidth costs.
If you are a techie, Amazon web services offer multiple systems that can be used together to create your own video hosting system. But it is cumbersome and has too many moving parts to be used regularly. It is better to use a good video hosting site rather than a DIY setup using Amazon Web services. If you want to test drive the whole video hosting, you can always start for free with YouTube.