I'm definitely not one who got to experience the vintage computing aspect until a couple years after it became obsolete. My very first computer was a Compaq Presario (5020, I think?) with Windows 98, even though I used my grandmother's older Windows 98 PC more (of which was custom-built and thus I have no clue what components were used inside it, all I can remember is that it used a beige In-Win case with a ridge embedded in the front bezel that housed the power, reset, and strange LEDs that looked like lines). I used both of these computers a lot when I was young.
Eventually I moved on and got a new Compaq Presario with a "blazingly-fast" Pentium 4 running Windows XP sometime in 2004. This computer had a lot of history with me, as it marked the first time I tried to fix something with computers. I think the DVD drive was shot or something, and I tried fixing it at the age of 7. I only got as far as removing it from the computer, but it helped establish my interest of computers.
As I grew to age 8 or so, I grew a large obsession with old computers. I really wanted Windows 98 again. Since we got a new Optiplex as our family computer just months before, that left me with the chance to have a computer all to myself. I decided that I wanted to install Windows 98 on the Presario with Windows XP. My uncle worked for IT at the time and gave me a Windows 98 install disk and product key. Believe it or not, I actually did succeed in installing Windows 98. Even though I couldn't figure out how to get drivers, I was still really happy to have a Windows 98 PC. I eventually gave the computer away sometime around age 10.
I still kept a small interest in vintage computers over the years, but it was all about building "modern gaming PCs" up until I turned 14. One day, I noticed that an old building was throwing out tons of old computers, and I was very interested in them. I managed to get 6 or 7 computers with several monitors, keyboards, mice, and all that. I had so many computers piled up that I really didn't know what to do with them. Several of them were the old Windows 98 PCs that I obsessed over as a kid. I was interested in rebuilding them, having some nostalgia, and just learning about computer history in general. This is what really introduced me into the hobby.
I'm now 16 and I love really any kind of old computers, especially the 386/486 era or even older than that. Nowadays it's out of pure interest and respect for computer history.