which macOS is recommended for a mac mini late 2014?

The performance of a ~seven year old Mac mini will range from slow to middling, depending on the hardware build specs chosen. Biggest differentiation from that era will be a build with HDD or with substantially faster SSD, and then whether base or faster with added memory. If you have a low-spec mini model with an HDD, then an external SSD on Thunderbolt or USB 3 can potentially help. But it’s still a ~seven year old Mac.

Right after an upgrade to Monterey things will be slow since with the upgrade process like reindexing the drives and redoing the Photos library consume resources which slows the Mac. These processes take hours and maybe a day or so

Whichever best meets your needs and is supported by the apps you need. Usually, that’ll be Big Sur or Monterey.