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I've built a few similar type of sites over the years using ExpressionEngine or Craft CMS's, generally where site members have various levels of access, i.e. "Free" (limited set of videos), "Basic" (selected range of videos) and "Premium" (all videos).
Vimeo is a good option for protected videos, they allow you to control where your videos are accessed, i.e. only via your web site domain name or IP address. That way you can restrict access behind a paywall or login.
Any decent web developer should be able to help you, perhaps do a search for people local to you so you can meet face to face if needed. I'd always recommend writing up a complete list of specifications you need.