My first computer was  a Tandy Color Computer 3 , 128K RAM, MS Color Basic, a cassette deck, and a B&W TV.  I got it when I was 7 for Christmas when Radio Shack was heavily discounting some of its older products.  I remember my dad gave me a choice between the CoCo and a Tandy 1000EX.  I picked the Color Computer because it had "color" in the name, which never really worked that well for me since I only had a B&W TV.  I still have it, but I wish I'd picked the 1000EX.
  
The first computer I purchased with my own money for "work" purposes was probably the computer I took to college in 2001:  Thunderbird 1.4 with a VIA Chipset, 512MB DDR RAM, 40GB HDD, SBLive! 5.1, GeForce 256 DDR, and a PCI NIC.  I upgraded to a GF4 Ti4200 the next spring.  Especially with the GF4, it was great, and I played the hell out of Ghost Recon and GTAIII with that thing.  However, not long after I installed the GF4, it started developing some serious problems that no one could figure out.  In retrospect, I think it was bad caps on the mobo and/or PSU.  I wound up going through several iterations of that system, including a Palomino 1600+ and a T-bred 2700+ and a GeForce 6800, and I used it until March 2008 when I replaced it with a Socket AM2 system running an Athlon 64 X2 5200+.  I still have the GF4 in my Win98 system.