Kurushi. Very cool game that still holds up today.

Alright... so I've got the SwanStation core downloaded on RetroArch and the CUE files downloaded for these six games: The Legend of Dragoon (as strongly recommended by @BraLoD), Final Fantasy VII, Final Fantasy Tactics, Ape Escape, Spyro the Dragon, and Crash Bandicoot. With time, I will surely add more (Omega Boost is one that has my attention, thanks to @Leynos), and as I get going through these titles, I'll keep these thread updated.

Thank you all again for your contributions here. :)

Hope you enjoy it, don't worry about grinding in LoD, the game is easy aside from a few fights on disc 2 and 3, just follow the story ane you'll get most level ups after boss fights, be sure to get the hang of the addition tho, completing them will make them stronger not only do more damage immdiatly in the fights, being good at them helps a lot. Also, don't go from a RPG straight into the other if you play it until the end, you might get burnt.

Also if you have never played either Spyro or Crash before, Crash is a lot harder, more focused on finishing stages, and Spyro is focused on exploring and finding stuff. Both are awesome games.

PS1 games are full of charm, hope the graphical barrier is not too much for someone only trying it nowdays.

Xenogears
Twisted Metal 4
Spyros
Crash Bandicoot
Tekken 3
Metal Gear Solid

That is very true. RetroRGB.com has lots of good information on what adapters to use. I use a Scart RGB cable from StoneAgeGamer. Avoid Pound Cables and other cheap $20 scalers. They suck. Either output to a CRT or get the Rad2X cables. 

There's still around 80 PS1 games that did age well. You have to focus on the RPGs and 2D games.

That is literally one of the worst ways to play PS1 games. Cheap emulation devices like that are not accurate at all. Go play a simple golf game with a meter, ala Mario Golf. Then try it on one of those emulation devices. You'll notice the horrible input lag. And the sound is often off. Especially on Sega emulators. 

As others have said piracy of old games is fine. 

A lot of emulators don't run these old games accurately. And as for improving graphics vastly, just use a proper upscaler. https://retrorgb.com/upscalers.html

Just a few suggestions that I didn't see on @firebush03 's list. 

Lunar
Lunar 2
Saiyuki Journey West
Legend of Mana
Ghost in the Shell
Wild Arms
Wild Arms 2
Star Ocean
Silent Bomber
Rival Schools
Oddworld 1-2
Parasite Eve 1-2
Guilty Gear
Megaman x5
Megaman 8
Arc the Lad
Front Mission 3
Breath of Fire 3
Breath of Fire 4
Persona 2 (Need to get the sequel on PSP for the full experience, as the sequel is a remake of a PS1 game we never got here.)
Bloody Roar 2
Dead or Alive
Need for Speed 3 (Running from the cops in a rainstorm is worth it!)
Tales of Destiny
Warhawk
Elemental Gearbolt (JP Edition Only)
Gundam Battle Assault 2
Jumping Flash
Jumping Flash 2
Nuclear Strike
Soviet Strike
Tail Concerto
Thunderstrike 2
Warhawk

👍 I’ll keep you posted once I’m started— for whatever reason, June/July feels like the right time for this game. It’s actually the highest rated game on the site I found the files from. Really looking forward to it!

Mega Man X4

If you need any help with the game feel free to let me know, there is some few things people can miss learning when playing it the first time around that could be cool to know, it helps a bit understanding the a few nuances that can help in battle and navigating around.

Keeping it simple:

• FF7
• Symphony of the Night
• Silent Hill 1

MGS also though you could also play The Twin Snakes for the slightly more modern experience.