If You Could Choose One System

[demon]

I'd choose the C=64 because of the overall balance between AV performance, flexibility and enormous catalogue.

[stayAwhile]

the amiga 600 yes it games are limited but that means your collection is easier to manage

[Negative Creep]

I'd be tempted by the SNES, but would have to go for the Xbox One, especially as so many 360 titles are now backwards compatible on it.

[nakamura]

PS2 because it plays PS1 and that is allowed because it's a standard feature.

Except that the OP specifically asked for an 8 or 16 bit system, so it isn't allowed.

If we're going to open it up to any system from any period in time, I'll go with a modern desktop PC that can emulate both the PS1 and PS2, and pretty much everything else that's been mentioned.

Whoops!!
Sorry, SNES then!

[miqrojamie]

Super nintendo without even having to think.

This. SNES holds so many great memories for me.

[Sega2006]

Sega Saturn, I don't care if it didn't have the 3D epics of the Play Station, it was my first proper console and having spent most of my childhood summers stuck on the Norfolk coast it plays the games that were familiar to me without the need for umpteen 20 and 10 pence pieces, RIP Segata Sanshiro.

[paranoid marvin]

A system with all the peripherals and all the games? For sure it would be the VCS; Id spend as much time admiring the box art and enclosed paraphernalia as playing the games.