These games are all also available on PC or in some cases PS4, and in a lot of cases are a better experience there, but I'll list them anyway incase you don't have a PC or don't have a good PC or whatever:Dark Souls - Action/Adventure(?) game where you play as "the chosen undead" to do whatever it is he does. I personally never paid much attention to the story in this game because it's one of those games where the story is built up and set around backstory stuff. It's probably explained a little by NPCs in the game but I dunno. You've probably heard about how ~unfair~ and ~difficult~ this game is, but personally I think it's more a case of the game just refusing to hold your hand at any point, telling you to be a grown up and beat the game yourself. One of the most rewarding games I think I've ever played in terms of "heck yeah i finally beat [boss]!". Also discovering everything in the game as you go through is super rewarding too, but again the lack of hand-holding might be you get stuck for a while sometimes, unsure of where to go.
Final Fantasy X/X-2 Remaster - Classic Final Fantasy duo, X and X-2, remastered for the current (last?) gen experience. All the graphics and music are updated. If you liked FFX, or like FF but never played X, or just like JRPGs, this is a pretty great value for money bundle because they're 2 full games, a side game that was originally only released in Japan, and an audio-book or something set after X-2.
Valkyria Chronicles - Strategy/Tactical RPG in which you take control of Welkin and (i think) Alishia(?) in a war against Gallia. Select units that best suit the battle, deploy them and then spend turns moving them up the field, shooting, hiding behind cover, etc. Really cool game, the art style is SUPER nice too, I recommend this game I think.
PS3 Exclusives:Kingdom Hearts 1.5 Remix - Contains an updated, remastered re-release of Kingdom Hearts 1 Final Mix, Kingdom Hearts Re:Chain Of Memories (Chain Of Memories on the main series engine, as opposed to a GBA one), and a cutscene movie collection of Kingdom Hearts 358/2 Days. Again, super good value for money because you get 2 JRPGs and a 2~3 hour cutscene movie of another. it's the first time KH1FM has been released in English too, it contains a ton of extra content the original didn't have in NA or EU.
Kingdom Hearts 2.5 Remix - same as above, but containing Kingdom Hearts 2 Final Mix, Kingdom Hearts Birth By Sleep Final Mix, and a cutscene movie collection of Re:Coded. Same deal as KH1FM, first time we get KH2FM or KHBBSFM in EU, both have a ton of extra content compared to the originals.
Heavy Rain - Alright, some people would argue this is more of an "interactive movie" than a game, since for the most part you just walk around and then do some QTEs sometimes, but it's a super cool... mystery solving game maybe? It has multiple endings (at multiple points in the game) so there's a lot of replayability I think, and the story is super interesting. You can get it pretty cheap nowadays too so I dunno, I recommend it a lot. Obviously since it's a mystery, don't google too much about it, lest the mystery be ruined for you haha.
ICO/Shadow Of The Colossus HD Bundle - ICO and Shadow Of The Colossus are both pretty critically acclaimed adventure games, in which you either have to guide a princess(?) to safety while fighting off Shadow monsters in ICO, or slay... 13 (I think?) mighty colossus by yourself, which you do by climbing them or stuff near them and slaying them. I feel like I'm probably underselling SOTC, imo the main game in this package, because I think it's truly a fantastic game. Definitely one of those "games can be art" games I think.
The Sly Trilogy - The wonderful adventures of Sly Cooper, updated and remastered for the PS3! Contains Sly 1, Sly 2 and Sly 3 (so 3 games for the price of 1!), this is a pretty cool... maybe action/adventure game? I'm super bad with genres sorry haha, which is focused a fair amount around sneaky sneaking but is a lot of fun. Has some cool minigames inside, and since you get 3 games you obviously get a lot of value for your money.
Metal Gear Solid Collection - (note I added this after Sly) WHEW talk about value for money sneaky sneaking games! This contains 8 Metal Gear games, including the original Metal Gear, Metal Gear 2, Metal Gear Solid, Metal Gear Solid: VR Missions, Metal Gear Solid 2, Metal Gear Solid 3, Metal Gear Solid 4 AND Metal Gear Solid: Peace Walker. If you're a fan of sneaky sneaky games with ridiculous, hard to follow plots but super fun gameplay and pretty great characters, this is THE bundle for you. You can also buy a
HD Collection containing only MGS2, MSG3, and MGS:PW if you're looking to sneak and barely be able to follow the story on a budget haha.
There's also a wealth of classic PS1 games (which you've obviously already discovered) that basically contains the entire FF backlog, which as a massive FF fan I highly recommend (especially 9 and 7).
Stuff I haven't played much but always hear recommended:Persona 3 and 4 are always really highly recommended JRPGs in the circles I hang out with online, they sort of mix social interaction game play like you might find in dating sims and JRPG dungeon crawling together into a super cool game, or so I'm told. They both have updated versions on handheld platforms but the originals are both probably good so maybe check them out?
The Disgaea series is also pretty highly recommended by those same people, it's a tactical/strategy JRPG where the emphasis is on insane numbers and leveling up and weird mechanics or something? I can't really do it any justice because I've barely played Disgaea 3, but they seem popular amongst the right crowd so they're probably right?
I think that's everything I can think of but I'll come back and edit this if I think of any more. If something sounds cool I recommend just checking out a youtube video for it haha, just beware spoilers!
EDIT: i've heard fairly good things about Ni No Kuni too, so that sounds like a decent pop. Uncharted are also pretty good adventure games even if I'm not really a fan of them very much myself. Think there are 3 on the PS3?