Try booting into Recovery Mode using Command + Option + R which should bypass the need to authenticate with your AppleID. You don't want your AppleID associated with the OS after giving it to someone else.
Do you have access to another Mac from 2007 to 2015? If so, then you can use the directions in the following Apple article to create a bootable macOS 10.11 El Capitan USB installer (read all the instructions carefully since the download & extraction of the installer):
Create a bootable installer - Apple Support
FYI, there may be exceptions for 2007 & 2015 models which may not support El Capitan....that is just a generalized range. You can use the following article to see which versions of macOS are compatible with various Apple hardware so you can identify & confirm a compatible Mac.
https://eshop.macsales.com/guides/Mac_OS_X_Compatibility
What is the exact model if this Mac? You can get this information by entering the system serial number on the check coverage page here:
Check Your Service and Support Coverage - Apple Support
Does this iMac use an internal hard drive whether a single hard drive or part of a Fusion Drive setup? If so, then you should either first enable Filevault & let it finish encrypting before you erase the whole physical hard drive. Or you can select the "Secure Erase" option in Disk Utility to write zeroes to the whole hard drive. This way someone won't be able to use a data recovery app to recover your personal files. If this iMac has a Fusion Drive and you wrote zeroes to the hard drive, then you will need to recreate the Fusion Drive afterwards.
Here is an Apple article with instructions for what you should do to prepare a Mac for sale (involves more than erasing it). Unfortunately that article assumes the computer is using an SSD or has Filevault enabled and overlooks the security issues if the computer is using an unencrypted hard drive or Fusion Drive which is why I added the extra bit above.
What to do before you sell, give away, trade in, or recycle your Mac - Apple Support
