You won't find the 'two-factor' option on the AppleId web site - this confused me for a while too.
To turn on the newer "two factor" authentication, go the iCloud system preference on your mac, click "account details" then "security". You can also do it on your phone in relatively the same place.
But then it still might not work. When I finally got two-factor turned on, the option to use the watch to unlock the mac disappeared. There's some trick to getting it to come back, but that part I haven't figured out yet (some people suggest rebooting all devices, some suggest logging out of icloud on the mac and logging back in). My guess is that it just takes some time for all the pieces to sync back up.