There are definately loads of good games for the original Playstation (or PSone), but unfortunately the popularity of the console attracted a lot of shite games as well. I hate the adverts you see (Well, I have seen) where they say 'Playstation now has over 1000 games' or whatever the number is, and they forget to tell you 90% of them are barely worth rental. Maybe this is harsh but I can't think of 100 good Playstation games right now (Then again I can't for any machine).
When I bought a Playstation I had already had a PC for a year or two and I wasn't expecting the graphics to be as good (That was compared to a old Pentium 2 with a 4Mb graphics card), but there were games I wanted to play which my friends had been going on about for ages(I'll give some later).
Generally I'd say steer clear of any PC ports for a start, the only reason for buying a PC game on the PS is for multiplayer (Like Quake 2, 4-Player splitscreen
). Everyone knows Black and White for the PC, some marketing idiot decided to put it on the Playstation. I haven't played it but I can only imagine how shite the graphics and speed must be, such an injustice to a great game. Also any game that comes out for PS1 and PS2 should probably be avoided IMO, since the PS1 version will always be cut down, for example Tony Hawks 4 or Fifa 2003, they just won't be the same game.
Finally I'll give you some good games I think you should look at, all I have played:
Crash Bash - Great little 'party' game, you fight in one screen arenas at various games, always 4 players of CPU or human.
Die Hard Trilogy - Ignore the sequel, this one rules. A decent third person shooter, light gun game, and street racer all in one.
Final Fantasy 7 - I looked upon this as shite for ages, but once I was forced to play for a hour I loved it. IMO the best RPG on the Playstation 1, but I haven't played 8 or 9 so maybe I'm wrong.
Gran Turismo - Or 2. The mother of all PS racing games, and arguably the best at its time.
Quake 2 - Like I said inferior graphically but nice for multiplayer splitscreen shootin.
Resident Evil 2 - I'm only saying 2 cos its the one I got. Great 3rd person horror survival game(s), only challenged by the likes of Silent Hill.
Soul Blade - My favourite beat em up on the PS. It has a nice storybook mode where you earn the characters weapons(some of which is bloody hard) as well as yer classic arcade and 2 player.
Time Crisis - Brilliant lightgun game. Nuff said.
Wu Tang Taste the Pain - Quite rare I think, a beat em up with weapons and in the vain of 'Thrill Kill'(Banned in UK methinks). Again a story mode to earn fatalities and stuff, great in 4 player brawls.
Other games I do not own but know to be awesome are basically Unkown_K's list plus Medal of Honour. Hope you have fun with your PS