Don
Get a SSD if you can afford it.
The OP mentioned a 4TB drive... I don't think a 4TB SSD is in the realms of affordability yet
I have one installed in my PS3, and if you use digital games it's fairly nippy.
The PS4 doesn't benefit that much from an SSD anyway - as Moogleys has said it uses RAM to buffer most operations and mask any physical loading times, hence loading times not improving much e.g. in Digital Foundry's tests.
The 2TB 2.5" Samsung drive is still the best option for the PS4 (without resorting to ugly addon casings, or worse exposed cables) and is fully supported.