I agree with maddox, a NAS is the closest to a plug-and-play solution and closest to your desired setup that you will find.
The problem with a NAS, in general, is processing power (on a budget NAS). They are essentially hard drives with relatively weak computers built into them, unless you spend a great deal more.
The next simplest solution is to get a small computer, such as a NUC, and run it “headless”. Then, plug in 1 or more external hard drives for storage. Such a setup can be small, energy efficient, and quiet, but significantly more powerful than a NAS.