So are we talking first computer, first built computer, or first gaming computer?
I can't say I've ever had a rig built with gaming in mind; honestly, I've tended toward consoles for my gaming needs. That being said, I've always had a taste for esoteric hardware and configs, so even though I've not built a GAMING rig, my rigs have always tended to be capable and to be used at least to some extent for gaming.
First computer: Texas Instruments Ti 99/4A
First built computer:
OS: Win 3.11
CPU: A Cyrix 486SLC if I recall correctly.
Video: 'Trident sumpin or other' LOL.
Case: 'Sumin scavenged from the trash'
Sorry Luta, but I just loved those descriptions, so I HAD to use them.
I actually built the system so that I could run some CAD software. At the time I was designing printed circuit boards and needed the software for both the pc board layout and also for Programmable Logic Array work that I was doing.