I never had an original PlayStation 👎. I did however have a PlayStation 2 and my first games for that were MX-2002 ft Ricky Carmichael and Gran Turismo 3-A-Spec.
Don't remember my very first PS game, but I remember hours of Pacman, Test Drive 5, Colin McRae Rally 2.0, and of course Gran Turismo 2 (which I miss so much it's almost unbearable [sarcastic])
I bought my PS1 myself, after the N64 I wanted was too expensive, in about 1999-2000.
First PS1 games were NASCAR '98 (still own), WipEout (still own), and Test Drive Off Road 2 (stolen).
Granturismo 2. My mom bought it for me and my siblings. Played the game all night. I remember my brother driving a FTO with a Castrol livery or something. The days.
Never had a psx or ps2 so my first ever ps game was Elder Scrolls IV: Oblivion
I have created a fairly large psx, ps2 and ps3 library in the mean time though, including every single gran turismo game
PS1: CART World Series
PS2: Kessen
PS3: NHL2K9 (though it came with MGS4)
None of them got near as much mileage as Iron Storm or Road & Track Presents The Need For Speed which were my twin original purchases for the Saturn I had before PS1. Well, over the years hockey might have come close to TNFS. It's a VERY short list that compares with my Iron Storm time played... most of the GT series is probably on it. Off topic but whatever.
Wasn't much into driving/racing games but I got Gran Turismo due to all the hype. Fourteen years(!!!) later and I'm still playing all 5 games (and the Prologue).