Hmmm, that's a hard one. I bought a lot of games back then. Mostly collections. The last one was Breathless. The firsts game I remember which I've bought were in a collection - black box, containing 4 or 5 games (black labels with white letters): Blasteroids, L.E.D. Storm...can't remember the rest tough. Anyone remember this gamepack and has more info ?
Second (or even first?) was Double Dragon 2, my favourite arcade game and a well made conversion.
I'm almost sure that the first game my brother bought was Evil Garden. A wonderful game. Still have it boxed here along with some favourites :-).