I agree with maflynn above, but would suggest you boot to "internet recovery" mode by booting and holding down the "command-option-R" (instead of just "command-R").
You can't erase THE ENTIRE DRIVE from the recovery partition, because you're BOOTED FROM the recovery partition.
I believe that you CAN erase "the entire drive" when booted to internet recovery.
Choose the secure erase in Disk Utility.
ONE PASS will be "all that you need". Anything more is pointless.
Then, get the OS installer going and do a completely clean re-install.
Once the install is done, you will be "dumped into" the setup utility.
At this point, I WOULD NOT BEGIN SETUP.
Instead, I'd just press the power on button and hold it down until the MacBook powers off.
Now, it's ready to "hand to" the new owner.