You might not need enterprise hard drives just quality regular drives that are HUGE. Enterprise drives can run 24 / 7 and have some other features to help with raid controlers and vibration etc. Stuff you might not need.
However, a good server would be benficial. Unraid, Truenas etc. Sure you can get a store bought nas but I suspect you will quickly out grow it and need more space. A customer server that you built would be more flexible and able to expand and even add some tools and such you might want in the future. Also provide a way to view and even download the videos when not at home. Send large video through dedicated links and not have to have Google or others watching over your shoulders.