How do you set up a new iMac from scratch after removing your old iMac?

The best way is to log in first with your Apple ID, and let it go through the authorizations and pull your information from you iCloud account. This will rebuild you new home user folder from scratch. After all that's done, if you have a time machine backup of your old computer, you could plug that into the new machine, and instead of restoring entirely from the old hard drive, you can selectively pick and choose what you want to pull over from the old computer. That way you're not dragging over clutter you don't want anymore.

If you don't have a backup, then you're starting off on you new machine only with whatever you have in your iCloud services: Contacts, Calendars, Mail, Keychains, etc.