As a young kid I remember starting with my brother's 386 (I think, maybe it was a 286). I'd largely play Lemmings, Wolf3D, and LucasArts games on that. Later my mom got a 486 laptop. I'd use that pretty heavily for anything I could get my hands on, which was lots of Doom, X-Wing, trying to make sense of XCOM, cheap shareware disks from bargain bins, etc. I was really young for most of this. No sound hardware, either.
I eventually got my very own cheapo prebuilt IBM Aptiva with a K6-2 in 1998, with paper route money. This was a hugely important machine for me, as it's also shortly after our family got internet access. I played a ton of stuff on that, but the biggest game was Duke Nukem 3D. It and ZZT/MZX, with their editors and massive mod scenes, drove a real interest in me for making my own content for games and learning how they worked on a deeper level. I also played Quake and Quake 2, not that they ran very well. My friends and I dabbled in online gaming via Heat.net and Internet Gaming Zone.
Admittedly, I also dug into "abandonware" a lot during this period. I learned about a shitload of slightly older PC games via abandonware communities. Emulation was a pretty magical thing as a kid, too, though still fledgling.
Some time in late 1998 I get my first exposure to Quake 2 running on a Voodoo 2. This was an eye-opener. I mean, I had seen the N64, I had seen texture filtering. But that obviously couldn't compare to 800x600 Quake 2 running at smooth framerates. Another friend gets a Voodoo Banshee and plays Half-Life, a game from the future, and I'm drooling. Around the same time my local game store gets an import Dreamcast demo kiosk. You could really feel GOOD CLEAN 3D visuals (at home!) taking off. My own PC could only cleanly play Jedi Knight and a few other Direct3D titles, as my poor ATI Rage II or whatever couldn't do OpenGL, lol.
A little later, in 2000 or 2001, I build my own PC with a GeForce FX, but we're outside of the 90s now. The late 90s and early 2000s were a big whirlwind. All this crazy emerging technology on both the PC and console fronts, all this time I spent playing both new games and digging into old games, all this time spent experimenting with level editors and mods and basic scripting, all this exciting new online play stuff. Very dense time in my memories.