First Amiga game I bought? Well, I think Tetris came with my brand-new A500 package, so I guess you could say that was it.
After that... Hmm. I don't really remember, either. I think it was a flight sim. I probably should have gotten Falcon (I later found out it was better), but I think I actually picked Chuck Yeager's AFT 2.0, as that had just come out. (Like 1989/'90)