If I remember rightly, the throughput on the PS4 is severely limited because it uses a USB->SATA interface. It's a waste of time buying an SSD.A 2TB SSD is around £200, or £170 - £180 if you keep you eyes out for the "daily sales" at certain retailers.
The £85 2TB Firecuda hybrid drive is a popular upgrade - again, straight swap out.
Easiest option is just plug in any USB3 external drive of your choice.
As suggested, I just got a 2TB Firecuda which i think was £99 at the time and that works great. Easy peasy, just get the OS on USB ready.