The 2012 Mac Mini will run High Sierra, and maybe Catalina depending on age.
10.13 High Sierra (beginning of APFS), 10.14 Mojave (end of 32 bit apps), 10.15 Catalina
Are tips for upgrading to each one. If you have a newer Mac, just download the installer, copy it to a flash drive, and bring it to the Mac Mini. The big problem you may be facing is AppleID for the App Store may be sending a request to your iPhone or iPad with a verification code for multifactor authentication. If it does you want to enter that code immediately following your password on your Mac Mini when logging in the App Store. MFA improves with Sierra (the OS prior to High Sierra) in the 10.12.4 version, and the code appears simultaneously on the Mac as iOS devices hooked up to the same AppleID and the entry field for the MFA code will appear on the device you login to for the first time on the AppleID.
Just an FYI, High Sierra and Mojave only have iCab as secure web browsing, where Catalina has Firefox ESR for secure web browsing. Catalina unfortunately requires you to upgrade all your apps and drivers to 64 bit release.
