Yep your to cool for this topic,and every one knows when your that cool and down with games, you would be above  a reply with a list of games and discussion of those games. 

Silent Hill if you never played before.
"Radio... what is going on with that radio?"

I really admire Silent Hill and MGS for both only using real time rendered graphics. And even more MGS for only using in game cutscenes. Something I admire a lot is when games only use real time graphics, I like CGs, but real time cutscenes are far more interesting. One thing that is a really turnoff too me is 7th gen onwards using CGI, unless it's something on a really big scale.

The best place to start with PS1 games is look at Squaresoft. Like, pick a game, any game, and there's a really good chance it stands the test of time in at least one aspect.

They don't have the same track record, but Capcom is another good publisher for the system. (Mega Man, Breath of Fire, Resident Evil, etc.)

Konami was still pretty good at this point and time too. (Castlevania, Metal Gear Solid, Suikoden, Vandal Hearts, etc.)

Oh yeah, Parappa the Rapper, Arc the Lad 1 & 2, Crash trilogy, Legend of the Dragoon, etc.

I came to this thread because I knew you would be here mentioning tLoD 

Silent Hill, King's Field, Spider-Man, Strider 2, Yu-Gi-Oh!: Forbidden Memories, Crash Bash, Soul Blade, Dead or Alive, Tiny Tank, N2O: Nitrous Oxide, No One Can Stop Mr. Domino, Parasite Eve, WWF Smackdown! 1 and 2, Tekken 2.

FF7, FF8, and FFT.
Xenogears
Suikoden 1 & 2
Parasite Eve
Resident Evil DC, 2, and 3
Vagrant Story
Metal Gear Solid
Wild Arms 1 & 2
Lunar SSS & EB

Legend of Legaia is literally the only PS1 game that I can play through (start to finish) every single time. It's just great.

But whatever you do, don't play Legend of Dragoon... I heard that game is garbage.

*makes eye contact with BraLoD*

Tears of joy, my friend.