Hmm, this is an entertaining question to answer.
The first computer I ever had contact with I don't even now the name, but it had a beautiful green phosphor screen. My knowledge by then was not enough to be able to differentiate between hardwares.
Other first contact, which impressed me a lot (and I mean A LOT) was with a Spectrum 16 Kb with a rubber keyboard. I saw my cousing writing long listings of BASIC and, as the code evolved, I could see a game shaping up. That was amazing.
Since then, I had contact with a ZX Spectrum 48 with plastic keyboard, and a Spanish version of this same computer created by Spanish hardware manufacturer Investrónica.
Another pleasant contact before having my own, was with an Amstrad PC1512, playing The Ancient Art of War. Wow! That was fun!
But my very first computer (after crying, and mourning, and desperately asking my parents for one for years) was a ZX Spectrum +2A, which had 128 KB of RAM and an integrated tape drive. As you can guess, it was one of the best microcomputers by then. Incidentally, Sinclair had been bought by Amstrad and the +2A was one of the first products they released.
The +2A gave me many good moments, but as everything in computer's life, it became obsolete. I managed to obtain a Commodore Amiga 500, an incredible computer with no rival by then. It was a system which still surprises nowadays, with its individual processors concept. My sister had a resplendent 386 in the other room, which was responsible of my first contact with computer viruses (Barrotes).
The story later is not that amazing. I acquired a 486 DX2 66Mhz with CD-ROM and a sound card to experience that thingy they called multimedia, although I was not very impressed since it did nothing the Amiga couldn't do (except for the hard-drive of course). And the list grows with a P100, an AMD K5 100, a K6 200, a K7 2 GHz... and now... tachaaan, I have been for a few years now enjoying the power of Apple computers, with a Powerbook G4 1GHz. After so many computers, just wonder why...