Sorry if its been mentioned, but Borderlands: Handsome Collection is a pretty excellent deal. Both games look almost as good as they do on PC and for the most part the port of the pre-sequel isn't too bad. I did encounter one or two minor bugs with the vendors, but nothing major.
There's always Samurai Warriors 4 if you're looking for a light pick up and play title. Lots of replayablility with the warriors games.
Spelunky is a solid platformer that you can also pick up on PSN. Be warned tho, its a rogue-like so perma-death is a thing.
Destiny combines RPG and shooter mechanics and I personally wouldn't classify it as a military one. I personally don't care for the loot system in this one, or the overall MMO feel, but its still a solid game.
Persona 5 is set to release this year, although it could be pushed back. There's also always the possibility that the english release won't be until 2016.
Transistor is a pretty solid game as well. There are some RPG mechanics with a tactical-real-time battle system. A lot of the games lore is hidden in item descriptions as well, similar to Souls games. Game is a little short though.
Bastion is also from the same developers who made Transistor. It was their first game(I think) and just recently came to PS4. Its a pretty solid action-adventure game, although like Transistor, a bit on the short side.
Tons of stuff on the PS4 to suit your tastes. If none of these appeal to you, I would recommend heading to GameFAQs and browsing through games there. That's usually what I do when I'm looking for something new to play that I probably havn't heard of before :D
“What I say is, a town isn't a town without a bookstore. It may call itself a town, but unless it's got a bookstore it knows it's not fooling a soul.” - Neil Gaiman
