Here's my journey of how I increased my PlayStation 4 (PS4) storage from 500 Gb to 2 Tb.
I bought a Samsung M9T 2TB 9.5mm SATA 2.5 inch Internal Hard Drive. Link to product Amazon. I feel that any smaller just isn't viable for serious use. The games with all expansions and dlc's take up a lot of space. And switching multiple games on the fly becomes really slow if space allocation and re-installation is involved. Even with a fast Internet connection it takes considerable amount of time before a game is ready to play.
After that get a flash drive with FAT32 allocation table format and free up around 900 Mb space for the playstation 4 update file. Here's a link to the full ps4 firmware update. It's easy to miss the small link to full version if you're going through the Sony website.
On the flash drive create folder PS4. Inside the new folder create another called UPDATE. Use names in all caps. Then download update file to this path. At the time I used update 2.51 which was 785 Mb large.
Now, after inserting the new hard drive into PS4, connecting flash drive to one USB and by wire connecting ps4 controller, hold the ps4 power button for 7 seconds. There will be a second beep, console will boot in safe mode. From the menu select option "Initialize PS4 (Reinstall System Software)".
I have PSplus subscription and I didn't need to back-up saved games or trophies. This could vary in your case. That is, I have automatic back-up enabled.
Hopefully all goes well and you should be able to enjoy bigger storage.
