The one caveat I've noticed is that if you buy digitally, the big games tend to stream the "rest" of their download while you play... but if you're not in THAT app playing, the rest won't be streamed. For instance, if you download Killzone from PSN, you're getting ~7-8GB. The games is much, much larger than that. So if you're playing say Resogun, that initial 7-8GB will download and install but it won't download the REMAINING 30GB or so until you're actually in Killzone, playing Killzone. That said, you likely aren't going to NEED the rest of that until you've already played the first part but if you say were "prepping" a PS4 for use in an area without internet (like say a submarine... lol), you'd want to leave the game running overnight one night if you weren't planning to actually start it yet. Same with Battlefield 4 that I've noticed.
This came into play for me as I tried to resume my playthrough of KZ on a 2nd PS4. My game was cloud-saved and I downloaded/installed Killzone. When I loaded it up, it DID auto-recognize that I was on Chapter 3 and start to download it, but I'd kinda already assumed it would be ready to go. While I was playing Chapter 3, it downloaded Chapter 4, 5, etc. and I never had to wait for it to install (it downloaded/installed faster than I could play it.)
It's really a tremendous system, but understanding how it works can save some potential frustration in fringe cases.