Back up to transfer to new mac

To be Safe - copy the files on Desktop to another external drive.

Move your content to a new Mac. If new Apple Computer is the newest Apple Silicon M1 version - strongly suggest using Migrate Assist at the first boot up of the new Computer. Also strongly suggest ONLY Migrate your User Account and nothing else. Remember, application and extensions from Older Version of macOS may Not Be Compatible with the Big Sur and especially the newest M1 CPU. Just because the applications worked on older versions of macOS does not automatically translate to work on Big Sur and again especially the M1 CPU.

https://support.apple.com/en-us/HT204350 and only migrate user account

Oh dear, I can foresee problems ahead for me. I have a late 2013 iMac 27" running Mac OS Catalina 10.15.7. I have decided to buy a new 24" iMac but will I experience problems in transferring data from the old to the new? I do back up to an external hard drive via Time Machine at the moment. Also, will I be able to connect the 27" iMac to the 24" via USB should I use Migration Assist, and bearing in mind the two different Mac OS systems which is the best way to transfer the data? Any assistance would be appreciated. Thank you.

Migrate assist is a wonderful tool. From Mac to Mac. It restores / moves nearly anything and everything; icons on the desktop, used folders, signatures and so on.

Thank you. Most helpful.

Welcome and enjoy the new machine.