The mid 2011 (server) Mac Mini has a standard firewire port. (FW800)
Perhaps you have an older firewire device with the original FW400 port? The FW800 port started replacing the 400 port around 2007. You can simply use a FW400 to FW800 cable to connect the older device and it just works.
Like this one for $5.
https://www.monoprice.com/product?p_...SABEgIBXfD_BwE
There are also little adapter cables (male/female) to adapt one end or the other.
Or... Does your device have that mini FW connector? (Usually found on DV cameras.) You'll find mini FW to FW400 cables for that. This mini connector is actually the oddball.
Also, this machine runs the current version of OSX. (Everything from 10.7 to 10.12) What it will NOT run is the older OS 9.