Because no one bothered to answer you in days I will take the whele from here, I hope this is okay for you guys.
1. If you just want to backup your data, I think a server is a little overkill. For backups a simple nas will probably be cheaper an suit you more. It is also less complicatet, unraid isn't so easy to start with an there aren't many guides for it. (it hase an awsome community tho) Get yourself a bearbone Synology with as many drives/capacity as you need for all your date. (plan about your future data too and don't underestimate it, it builds up quickly) https://www.synology.com/de-de/products/series/home
2. If you still want a proper server you need to give more information what exectly you want to use it for. I also would recomand to ask this question in the unraid forums. There are people who know much more than I do.
3. For quietnes I built my PC in an Fractal Define R5, with 3x beQuiet! Silentwings 3 PWM (Fans set to silent mode in Bios) and WD Reds. The whole thing is near quiet, only the disk spinning makes a little noise. I put the Server between my couche and wall, in a side fliped shelf.
4. proper shutdown = Shuting down windows (or unraid) normaly over the proper comand. In windows that would be via the the windows menu -> Shutdown / Reboot
improper shutdown = Shuting down your PC/Server by disconecting the power cable or some kind of forced shut down. This will not destroy anithing but data can get lost, especially for unraid oder any kind of server. + unraid will check all your date. this can take hours or even days. Its recomendet to have an UPS for your server.