When I was young we had an NES, I don't really remember playing it. I do have distinct memories of watching my father play Zelda 2 though.
We later traded that in from the Genesis(Mega Drive). I played a bunch of Sonic. Ys3 was probably my favorite game on the system though.
I know you said to not go past the 16 bit era but, the first system I owned was the PS1. I got it for my 10th birthday. I remember felling bad for my father because the price for the system 6 days later and he didn't have a lot of money.
All my old systems are gone, but I have since when back and bought NES and SNES. My little sister also has a genesis now.