The nice thing about PS4 is that you can play a lot of the games from PS1-PS3 as well, often as remakes or remasters. I actually like PS1 - PS3 games a lot more than the newer PS4 ones, but if you've never played any Playstation, then there is a huge mountain of fun games out there. Here are some "PS4" games I really like (many of which are from previous generations):
Final Fantasy 7 - 12. (including X-2)
Uncharted 1 - 4 (1-3 are in a collection)
Shadow of the Colossus & Ico
Every Dark Souls game
Dragon Quest 8 & 11 (haven't played 11 yet, but 8 is awesome)
Dragon Quest Builders
Probably a lot more I could name, but at this point I'd have to look which ones are on PSN to be sure. There are tons of great indie games out there too though, a lot of them from previous generations. There is really a huge mountain of great games out there if you've never had a Playstation before. I am saying this as someone who is hugely dissatisfied with the PS4. For me, I see a bunch of games I've played before (or something similar). But for someone who has never had any Playstation before there is many years of enjoyment there.