Because I have the nifty new toy known as my new-to-me PS4, I now need games to play on it. Most people recommend AAA titles which is all well and good, but I'm aware of most of those. What interests me most are the offerings on PSN.
I heard about Never Alone from Cary when he reviewed it for GamerDad, so that one was on my radar, and then I saw that Joe had played it, too, and he happened to be online when I was game shopping and was willing to answer my questions about it. Bought it, played it, and enjoyed it.
Did a quick search for ten best lists and discovered Firewatch. Another former 1upper with similar taste in games gave it a thumbs up, and that, too, was bought, played, and enjoyed.
Other games that I've seen or had recommended and scribbled down are:
Feel free to make more suggestions. I like puzzles, platformers, adventure, RPGs, visual novels, and pretty much anything story-driven without a butt-load of shooting.
I still haven't gotten past a certain point in Broken Age, but i liked its sleepy-time visuals and duel storylines. I just couldn't find the thing to go in the thing to go forward at one point, and that's basically a point and click "find the thing or things to build the thing to give to the character to proceed" kinda game.
I think i may have already mentioned everybody's gone to the rapture. If not, i can tell you what i thought again.
Into the woods is a newer one you might like, but i haven't played it. I just kinda want it. I assume you're aware of inside and abzu(?) is by the people behind journey and flower i believe ( haven't played that either, but patrick talked about it on the best of 2016 nwp podcast).
One of the interesting games i got for ps + you may enjoy is grow home. Basically you grow a bean stalk as high as you can to climb as high as you can on a planet.
Xeodrifter was a fun Metroid knockoff.
I'll look at my psn library and see if there's anything else you might like. Or you can look (i think) and ask me about anything you think you might like.
I think Life Is Strange is really good! Also first season of Walking Dead TellTale. If you like story adventure games that require a bit more exploration and interactivity. Alsot Wolf Among Us is my favorite TellTale game. They go on sale fairly regularly since they are older games now. I liked King's Quest too. Very retro with current gen graphics.
I liked Axiom Verge a lot which is a mix of Metroid 1 exploration with Contra guns, if you liked either of those types of games.
Dark Cloud-PS2 on PS4 title
Dragon Quest Builders
God Eater Resurrection
Sadly thats all I can think of at the moment
Well, I just joined Gamefly again and put stuff like Nioh, Tales of Berseria, Yakuza 0, Horizon Zero Dawn and The Last Guardian on there for PS4. I wanted to put Ys Origin on there too but it's download only.
Life is Strange
I Am Setsuna
I think you would dig the Witness, but I heard some of the puzzles are pretty tough. Of course, you are a ranger! :)
Ahem - Myst and Riven. Do game puzzles get harder than those?
I don't know. I haven't played those, but I have heard the Witness is hard. Might be right up your alley. Very beautiful to look at too.
The walkthrough book for Riven is incredibly thick for a game that came out in 1997. Myst was also almost impossibly tough. My brother and I used to get together and try to solve the puzzles after we had Sunday dinner with our dad. I don't think we ever beat either game.
well, nowadays there's this thing called the internet which makes it easier than ever to cheat! :p
When getting PSN games, wait for the sales. You can get many of the games half off or more sometimes. I bought my PS4 almost 2 years ago and in that time bought a crap load of games. All of them were on sale and under $10. I may of spent full price on 1 or 2 games, but they were under $20. 
I'm pretty new to the PS4 scene, too. But I think you'd really like Tearaway: Unfolded. If you like point and click adventures, I'd suggest downloading The Little Acre. Shantae: Half Genie Hero is a fun 2-D platformer. Atari Flashback Classics vol. 1 and 2 are nice collections. I don't know how you feel about Minecraft, but I also think you'd really like Dragon Quest Builders. I haven't played my copy yet, but I did like Odin Sphere on the PS2, and they re-released it on the PS4.
As others have mentioned, if you like games like Firewatch you'll probably also enjoy Life is Strange. Gone Home is another 'walking simulator' game that I enjoyed, and it recently came to the PSN.
For puzzle games, I'd recommend The Talos Principle. It's kind of like The Witness, although the puzzles are a little easier (The Witness can get extremely frustrating). I'd compare the puzzles to Portal, where they are just hard enough to make you feel good when you complete one, but not so difficult that they feel cheap. Its also got a pretty neat story to go along with it.
Since it is the most recent game on the console I've played Telltale's Batman. I also liked the most recent Ratchet & Clank, and inFamous First Light (I liked this game more than the full on inFamous Second Son).
I played Song of the Deep last year. Great little game. You might also want to take a look at SOMA. Sherlock Holmes: Crimes and Punishments supposedly has good stories even if the mechanics are a little wonky. I have that one but haven't played it yet. If you have someone to play with, Broforce and Magicka 2 are both great, dumb fun (yet challenging) co-op games. Perhaps a little shooty, but I'd recommend them. And there are two remastered LucasArts classics on PSN, Grim Fandango and Day of the Tentacle.