Depends how "technical" you wanna get
We had a master system, but twas my mums. But first games on that were Teddy bear and or Sonic (cant remember which was first), then we had a megadrive - again hers. And all games, hers.
But then we bought some games, and I got to choose one for me

, so twas my first game in that sense, and that was rainbow islands, which i got on my
psp for ma megadrive(genesis) emulator

Also bought the new version for me DS, but was rubbish

(am hoping the
PSP version, when its released, is better

)