What you need to move, depends on WHERE you keep things.
If you keep everything in your home folder, you could just copy the home folder to an external drive of some sort (hard drive, USB flash drive, etc.).
If you keep things "spread out", you'd have to copy them to the backup drive "by hand".
Or... get an older copy of CarbonCopyCloner (I think the version you'll need is 3.4.7), put it on the iMac, and use it to create a "clone" of the iMac's drive to a backup drive. The backup will be mountable on other Macs, and you can get the things you need from it.
Important:
You may run into "permissions problems" when moving things from one Mac (with one account) to another Mac (with another account, even if the name is the same).
To get around this, you mount the icon of the drive on the desktop, then bring up the get info box (command i) and down at the bottom unlock the lock icon with your password and put a check into the box "ignore ownership on this volume". That will fix it.