How do I clean up my Mac before I transfere my files to a new Mac?

Click on the link to read how to...

Move your content to a new Mac - https://support.apple.com/HT204350

Some prefer using a Time Machine backup.

Back up your Mac with Time Machine - https://support.apple.com/HT201250

Restore your Mac from a backup - https://support.apple.com/HT203981

Learn how to transfer all files from your Time Machine backup to your Mac

If moving from older computer running macOS 10.12 Sierra to a New Computer probably running Big Sur . notation this is a Big Jump. Big Sur like Catalina do not support anything 32 bit and that includes Application, Extension and Drivers and there is no workaround for this. One will have to inventory the existing application, extension and driver on the existing Sierra computer and see if the Developers have Big Sur compatible updates or upgrades. None of these item should be transferred from Old to New as they will just not work. As for the Method to transfer - what might you have in mind ?

What makes you think it needs "cleaning"? For me most of the organizing my computer needs is me sitting down at it for a day and moving files to sensible folders. I think you know how to do that.