Got yourself a PS4, huh? ;)
If you're a fan of FPS, then definitely check out Killzone: Shadow Fall. It'll show off the graphical power of your new system, and has a pretty good single player campaign. I haven't really touched the multiplayer yet, so you'll have to research that component of the game for yourself.
I can honestly say stay away from Battlefield 4 until they have ironed out their multiplayer connectivity issues. It has caused frequent disconnects during ongoing matches, and the lag can become an annoyance at times. It's a real shame because when it works, 64 players playing on the same map is quite a sight to behold.
Regarding the racing genre, Need for Speed: Rivals is a great addition for one's PS4 library. The game bases itself on servers that allows you and 5 other players to racing around this huge fictional world. The racing events that they partake in all happen in real time, meaning you'll able to interact with their ongoing race that happens to cross with whatever activity you're doing on the same route. You can also join their event and help them accomplish it or compete in it yourself.
Feel free to add me on PSN. FoxnHurley- (include the dash)