"In my opinion, most influential game console in history (the N64)"
Full disclosure: The first game console I ever played and owned was a NES.
I would guess that the original NES was the most influential game console in history. Other than Goldeneye and Perfect Dark, all the characters from the other games you mention were either started on the NES or SNES. Super Mario Bros, Contra, Zelda, Metroid, Mega Man, Final Fantasy... they all started on the NES or were at least brought to home consoles by it. Super Mario Kart and Star Fox were both started on the SNES.
Frankly, there weren't any game consoles before the NES that were so popular and brought video games into so many households. The N64 was just a very good console in a progression of good consoles.
But I suppose I'm biased