A lot of games haven't aged well, so I'll recommend some that I think have, as well as slightly less.common games
Parasite Eve 2
You will have to adjust to old Resident Evil style Tank Controls, but once you do this game is a proper survival horror experience.
No need to have played the first game, story is easy enough to follow.
CastleVania Symphony of the Night
Some think this is the best of the castlevania, it's open world and still looks great. Controls are spot on it's very hard but feels fair, similar to the diffelculty of Dark Souls.
Chrono Cross
This is a must, it's a classic JRPG a sequel to the SNES classic Chrono Trigger.
I liked this just as much as Final Fantasy VII back in the day.
Encaptivating storyline, endearing characters and an amazing soundtrack on par with Final Fantasy VII.
This game hasn't been released on any other platforms, so PS1 is the only place to play it.
This game is in my top 3-5 favourite games of all time it's so much fun, and a real time sink.