So long story short, found a PS3 at a thrift store for $20 (specifically the OG model with PS2 backwards compatibility), decided what the heck, and bought it so I could check out some games I missed out. Not too familiar with the system's library so I could use some recommendations.

DO NOT SUGGEST:

First person shooters

Games I can get on PS4 or PC

GAMES I ALREADY PLAN TO PICK UP:

Persona 4 Arena

Persona 4 Arena Ultimax

Catherine (even though I already beat this game)

Demon Souls

NieR

Drakengard 3

Ni No Kuni

Metal Gear Solid: The Legacy Collection (Never played a MGS game besides the first one believe it or not.)

Yakuza 4 is a good option, since it also tells you the story of all the previous three Yakuza games, so you can play that one without any issues.

Infamous 1 and 2 are a must.

Heavy Rain.

Vanquish (multiplat with 360 but worth getting it)

Tokyo Jungle.

Red Dead Redemption (same as Vanquish)

Puppeteer.

3D Dot Game Heroes.

Shadows of the Damned (same as Vanquish)

I think you have enough to start here.

Ratchet & Clank Future: Tools of Destruction and Ratchet & Clank Future: A Crack in Time!

Really good games. A Crack in TIme is my personal favorite Ratchet game.

Alice: Madness Returns and Sonics Ultimate Genesis Collection.

EDIT: They are probably on the PC. Forgot about that...

There's a really rare game that not many people know about, I highly recommend it.

Sonic 06.

Ninja Gaiden Sigma is a really great game, I'd definitely recommend that.

Fifa 08 to Fifa 13

Serious: White Knight Chronicles I & II, Eternal Sonata, Ico/SotC HD.

Ico & Shadow of the Colossus Collection.

Trials of Cold Steel 1 and 2, if you love persona then look no further than these games.

Don't forget Infamous 2 DLC called Festival of blood. it's probably my favorite Infamous.

I second Puppeeter, a very charming game.

Ico and Shadow of the colossus (still not released on PS4 technically...)

Jak and Daxter 1

GT6

God of war Ascension

Outland (it's on PC but the PS3 version is great, underrated game)