OP:
What you need to do is:
1. Boot to INTERNET recovery (this IS NOT "the recovery partition"):
Command-OPTION-R at boot
You'll need your wifi password IF you're connected to the net via wifi.
The internet utilities take time to load, be patient "as the globe spins".
2. Once the utilities load, open disk utility.
3. VERY IMPORTANT -- go to the view menu and choose "show all devices".
4. Look at the list on the left. The top line is the physical drive inside.
5. Click on the drive and click "erase". Choose APFS, GUID partition format.
6. When the erase is done, quit disk utility and open the OS installer.
7. Start clicking through. The Mac will restart one or more times, and the screen may go dark for a minute or more. Be patient.
8. When the install is done, you should see the initial setup screen. DO NOT go further.
9. Either quit setup (see if there's a menu option), or (if no menu option), press the power on button and hold it down continuously until the display goes dark. It's now ready to hand to the next owner, who will see the setup the first time he boots up.