Memory required for Time Machine backup on Mac mini

If you mean how much storage should you have for TM then get one that is 1-2 TB. Remember 256 GB of storage is VERY VERY little, Time Machine should be 2-3 x the capacity of the total storage.

“time machine backup memory: how much memory should you reserve for time machine backup on external drive bought 16gb unified, 256 ssd m4 mini”

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Time Machine Backups and Memory:

Memory (RAM) plays no role in Time Machine Backups. As for how big of storage of a hard drive to get, I recommend one that is already twice the internal storage. It is important that you create backups prior to making any major changes to my Mac such as update and other software installs.