You don't need a NAS, really. My setup is a second-hand i5-7300U fanless mini-PC I got for $90, 2 x second-hand 4TB HDDs, and 2 x USB 3.5" enclosures. It's messy but it works... I haven't measured power in a bit but I reckon it pulls around 20-30W, which is around $15-20 a year at my current prices.

We back it up daily using restic to an old 2TB NAS that's at my parents place + the occasional manual backup