A note on the fans specifically, you can buy quiet fans. In general, the larger the fan, the lower the speed and the quieter it is. You can also setup fan curves so they are only doing anything of note when the computer is pumping out heat (given your statements, that would be basically never).

The electricity usage is a pretty notable thing. Though, if you take the graphics card out of a desktop (use integrated graphics, a dedicated graphics card in a server is just wasted electricity) and set the OS to power saver (this mostly means it won’t boost the CPU to higher clocks), it really won’t use much power. Compared to buying dedicated NAS hardware, you may never recoup the energy costs between the hardware you have and the lower-power hardware you need to buy.