As it is going to be a video sharing website it will require a lot of capacities to handle heavy video files, different formats, therefore the dedicated server would be the best option. However, as you begin from scratch, I believe, you won't have users to generate a revenue to cover a dedicated server, let alone the promotion of your website. So you can start with a shared server or VPS and upgrade later. 

Oxwall has default video plugin for embedding videos, however if you want your users to upload their own videos you will find some 3rd party video uploading plugin in our store:  http://www.oxwall.org/store