Just quick format. A full wipe is unnecessary. Since it's going to you're dad I doubt he's going to try to recover any data you had on the drive. A full wipe just makes it harder for data recovery, but it also takes much longer.

Full initialization process with 500GB stock HDD took in my case not more than two hours. I just got back to my ps4 after around two hours and the process was done already showing choose language screen.

A quick format on a HDD will generally just get rid of the file table but leave all the files behind where a full format will attempt to delete all the actual files too, there is also low level formats which will specifically write 0's to every bit of data on the HDD, can take days though.

But yeah think of quick format as the HDD forgetting where the files are on the drive... they're still all there, but like a person above said, your dad is unlikely to go trying to rebuild the file table to recover your files from the drive lol and as your father uses the system it will start to fill up the drive and overwrite the data of your files as it fills up the drive as though they weren't there.

That's a good explaination thanks.