CUPS is the most common printer system.
For arch, CUPS needs to be installed pacman -S cups
https://wiki.archlinux.org/title/CUPS
Cups comes with some systemd unit file. A socket activated style, or simly enable and start the service.
CUPS have a web management protal, at localhost:631
User need certain previlidge to be alled to manage / control printers
Cups have a config file at /etc/cups/cups-files.conf
In the file, there is a line of SystemGroup xxx xxx. This determent which group of users can be admin of CUPS
(On some system group lp or lp-admin would be in this)
For example with arch, this list only contains sys root wheel. Which means the actual admin user need to be added to one of these groups.
brother printer would need some additional drivers. brlaser is a good one to go with, available on many pcakges.
Server side is the machine that already have access to printer (like usb connection)
according to https://wiki.archlinux.org/title/CUPS/Printer_sharing