How to remote access a new m4 Mac mini?

Please explain in much more detail what you need to access? If it’s simply some files, then put them in iCloud and use iCloud to access them. If you are trying to run apps remotely it’s possible using remote access however please don’t expect much in the way of performance.

Without details all you are going to get in very general answers.

you can look into solutions such as

TeamViewer—The Digital Workplace Platform

and there are others it really depend on how much you are willing to handle yourself and how much you will let others handle at a price

of cause you will need to set the mac not to fall too much asleep to save power, to be able to connect to it.

One option is Apple Remote Desktop. See: Install and set up Remote Desktop - Apple Support

and

Apple Remote Desktop User Guide for Mac - Apple Support