I just recently upgraded my PS4 HDD to a 2TB drive and thought I'd share. The process was surprisingly easy. I ordered an external HDD, cracked it open and pulled out the drive. I put that in the PS4 and it's working great. Instead of going into great detail about the process, I'll post a video done by someone else on the subject.
The one I ordered, and recommend, is this one: Seagate Backup Plus 2 TB Portable Hard Drive STDR2000100, Black
If you give this a shot, let me know how it works for you.