I've now used three iterations of mini as servers. You mention having no budget which leaves lps out of the question, this will be greatest limitation of using a mini.
I could provide much info, but you may really be better off with raspberry.
Still, just for comparison sake, get 3rd party app wipe for OS, even though latest Mac OS doesn't allow complete wipe of many needless apps integrated within OS, stupid. Disable system integrity protection (DIP) via terminal, this will be nice upgrade, disconnect wifi antenna if not needed. Beyond this, fastest processor, I7 preferable to I5, PCIe preferable to sata.
Sans lps, the second greatest limitation with mini is usb rendering is crap. To bypass one needs separate streamer and bridge thunderbolt as second ethernet port.