You can buy a vps, but having cPanel on that vps might have some additional costs to it. In case if it is suitable to you, it's good or else you can try for other control panels like virtualizor and stuff. Have a look at what hosting providers are providing to you.
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I already have a VPS, and for my website, its an overkill. The website has very low traffic and is used for my family and friends only.
Mine too - but I've tried several reputable shared hosts now and they were all slow, unreliable and insecure. If you can't find a suitable host that specialises in media hosting (what's wrong with Vimeo?) then you'll probably need a VPS unfortunately.
A cheaper option if you don't need bandwidth or reliability and you have a decent internet connection would be a device such as a WD MyCloud (http://www.wdc.com/en/products/products.aspx?id=1140) that can be opened up to friends and family. 3 terabytes of storage, a streaming server and quite cheap. I have one of these as well.