A note on the fans specifically, you can buy quiet fans. In general, the larger the fan, the lower the speed you can run it 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.
If you don’t already own one, a Kill-A-Watt is a great tool to have. Tells you how much energy a device is using. Biggest thing I found was my TV had a vampire draw of 15W. Literally draws 15W while off. This got the TV put on a power strip I turn off when I’m not using it.
Now, with all that said, sometimes you just want what you want. And there is nothing wrong with that. My goal here is to make sure you don’t feel you have to pick one option over the other.
The UPS should have a USB plug in the back. Plug that into your computer and it will read the battery status as if it was a laptop. Then in your OS, set the standard shutdown options when low on battery.