The first game I remember is Black Magic (at least I think that was the name), on my friend's Laser 128.
The first game I bought was Betrayal at Krondor because I was a fan of the author. I didn't even have a computer yet. After having it about a week I bought my first computer... a Leading Edge 486SX25. I think Leading Edge might of been a Future Shop in house brand. Not sure though.