I have a PS2-compatible PS3, and a N2DS XL. The 2DS is a fantastic little emulation machine, and the PS3 plays three generations of games from my youth well into my adulthood. Between those two devices and my desktop, I'm pretty much set for any game.
That said, my favourite way to play old games is The Internet Archive Console Living Room. The bar to entry is so incredibly low (any modern browser is good enough), and you can share random games with people just by giving them a link. For example, would you like to play my favourite game of all time? Click here and click the power button. Controls are below the game.
It's really vague, it doesn't define its terms, and despite all of that it somehow still manages to be self-contradictory which is frankly impressive.