Shared hosting is definitely out of the question as the resources you consume as far as CPU will likely be in violation of most hosts TOS (using resources to the point it affects other customers). A VPS would be better but if you get a lot of traffic and a lot of videos streaming you will run out of disk space and CPU fast, and also may begin affected the host node, most hosts won't allow this.
If your site is just starting and is not that busy and doesn't have a lot of traffic or content, a VPS will be fine until the above starts happening. To plan ahead consider which provider and dedicated package you want so you can order and migrate everything to it once your VPS outgrows you.
This is where a physical dedicated server makes the most sense since you can use the full resources of whatever hardware you choose. I would actually recommend running a VPS on the dedicated and allocating all the resources to it, this way your host node cannot be hacked due to issues with your website or other exploits and you can live migrate to a more powerful server in the future.
This is further on of course but if your site becomes very large and successful you'll want to consider a public or private CDN and also load balancing your sites and videos across multiple servers.