Well, it was not really mid 1999 and I am not really sure if it was Christmas 1999 or 2000. I am 19 slowly approaching 20 so I was just 6-7 at that time. Our first multimedia family computer was a Pentium III based Celeron Coppermine 633 Mhz, with an nVidia RIVA TNT2 32 MB graphics card and 64 MB RAM. Except for the slightly anemic RAM it was a wicked machine, never remember any lag or stutter in any games from that period, and it played DVD quality 720x576 DivX movies without any troubles. I used it until 2004, since 2002 it was upgraded to a 1 Ghz Celeron, 320 MB RAM, and Geforce 2 MX400 64 MB, run Windows XP like a charm after this upgrade, played Morrowind on it without any lag or stutter.
This is slightly off topic, but before that we had a 1991 computer with a 40 Mhz Am386 with 4 MB RAM and a Trident SVGA 512 KB card, which was my introduction to computing. From reading both the 1992 and this thread, both of our computers were above average. I guess this is because my father tended to always buy the best (not extremely expensive through) electronics and not upgrade it much after that. I guess this stems back from the communist era (I'm from Slovakia, formerly Czechoslovakia), when electronics were really rare in the shops so when you bought a TV or a hi-fi system you expected to use it for decades and so it was much better to spend the money on the "top notch" system rather than use a piece of crap for the next 20 years.