My first "computer" would be the Dragon 32.

My favourite game on it was probably UGH where you'd run around a track stealing eggs and avoiding dinosaurs iirc.
After that I got a system with Windows 3.1. Used to play a few dos games on that like Prince of Persia and the Blues Brothers. There was a game that would let you make a colony on the moon too, which I really enjoyed.
Then windows 98 (still have that one here). Used to play Age of Empires 2 and total Annihilation on that one a lot. I started using DBC on this system.
Then an XP system which I've played a tonne of games on and upgraded quite a bit. This was when I started using DBP. I still use it today for Counter Strike Source.
Then a Vista laptop. This was mainly so I could code and game on the move. I started looking into other languages with this like C++ with the GDK.
And now I'm using an XP notebook; an Acer Aspire One.

I really love this little thing. :')
Oh wait; you only want the first computer?