I purchased my first server for the home a few months back and was in a similar position as you not wanting something very loud. If I purchased a server and it sounded like a jet taking off all the time my wife would unplug it and I would be stuck trying to resell it.
I liked the price that older HP, Dell, and Lenovo servers were going for on eBay but I read to many forum posts of people trying to use non OEM hardware on these servers and never being able to get their systems quiet again. For example on the HP servers if you use none HP drives, controllers, NICs, etc. the system may not be able to detect sensors on them and will run all system fans at full speed.
Based on other’s issues with these top branded servers I decided to focused on systems from Super Micro, Intel, and others. I wound up buying a system from the for sale forum here on STH and was able to get an idea of the server’s noise from someone with working hands on experience. It is an Intel S2600CP based system and after its initial post is really quiet and have had no issue adding hardware to it.
Larger server are normally going to be much quieter then smaller ones. Newer generation servers offer lower power consumption. The list of considerations can go on and on but for someone to give you recommendations they will need more details such as budget, size, and what you plan to use the server for.