This year Saint Nicolaas and his half brother Santa teamed up and decided to make our daughter happy with a PS4 slim.
It will come with FIFA18 (Nobody asked for that, but it comes for free) COD WWII for the mother, Battlefield 1 for the father and Rainman legends for daughter. Since this is our first console since the Jaguar I have no real idea what's out there that is fun and playable for young kids. We're on a budget so we only use the standard controllers for now.
A lot depends on what she is into.
Look at Tearaway unfolded, maybe Knack or Knack 2. Little Big Planet, Just Dance, Unravel (A cute platformer where you play as a yarn creature)
My daughter loves Minecraft and "The Escapists (1 & 2)".
I bought this $2 game on PSN, "Catlateral Damage" where you play as a cat and do cat things like swat things off shelves, jump to high places, go in boxes, etc. My daughter loves it.
Also maybe look at games like "Flower", "Bound", and "Abzu". In Flower, you play as the wind and blow flowers around the fields. It's much better than it sounds. Bound is a platformer where you play as a sort of ballerina. Abzu, you are a diver exploring the ocean and solving puzzles.
Finally, PS4 comes with something called "Playroom" built in that is fun for kids. I think some of the features need the camera though. BTW, the camera accessory isn't a must have unless you want to get VR. Only a handful of non-VR games use it.
Make sure to check PSN, lots of games there that are never sold in stores.