You can either do a system backup to the 2TB external drive and then restore that backup on the new PS4, or use the network system transfer where you connect both machines with an ethernet cable and then run the transfer utility. Ethernet would take fewer steps but will probably be pretty slow. I'd set it up to start transferring before you go to bed.
Either way, just do a full factory reset on the old PS4 after you're done transferring, to wipe all your data from it (and if you really want to be sure, you can then reinstall the OS from a USB stick afterward). All this stuff is pretty easy to find in the settings, but Sony should also have tutorials up that you can find with a quick google.
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