I would have recommended Resogun, Tomb Raider, and Assassin's Creed IV as the three best games for someone not into FPS shooters. Resogun because every gamer should play and enjoy that, and the others because you like action/adventure games that Naughty Dog is well known for (enough for you to buy a console).
If you have a PS+ subscription, then don't worry about buying any more games until some new game that appeals to you comes out. In meantime you can play Resogun and then you can also try out the F2P games available on PS4 like DC Universe Online and Warframe.
Also, keep an eye on additional PS+ free games each month. For instance Feb will have Outlast which is a survival horror game without any combat... basically you have to run and hide to survive.
EDIT:
For upcoming games, I am looking forward to:
Thief in Feb
inFamous Second Son in Mar
There will definitely be more games beyond Mar, but I don't normally look that far ahead (not much point sitting and waiting for stuff)
