Honestly, it would be easy for me to say something like Sega Genesis or PS2. But, the truth is...when you're talking about any old console, most of those iconic games can be played on the modern consoles anyway. So, it would feel shortsighted to choose something like that. In terms of iconography, aesthetics, and just how I feel when I look at a system...it definitely is Sega Genesis. Honorable mentions to PS and PS2, and probably 360 as well. I have nothing but love for all of those. But, I have to acknowledge that I've honestly played something like a modern Xbox One a lot more than I ever played those other systems.
It's just too difficult to pin anything down. I've played a lot, and I've loved a lot. I was really fond of Gamecube, and Gameboy Advance, and DS, and now the Switch. I have great memories with all of them...and I'd honestly say that almost every console I've ever owned was "my favorite" at the time that I was playing it. I know that's a terrible "non-answer"...but, it's the truth. Lol. The modern ones allow for backwards compatibility, so they are objectively the best. When I'm playing a modern console, I'm fully tuned into that one system, and I'm having a great time. So...that's my answer.
Right now, I'm playing Last of Us 2, so I'm playing my PS4 almost every day...and I'm in love with everything about the feel of that system right now...but, under normal circumstances, I would never tell anyone that PS4 is my favorite system...because it really isn't. I play Switch and Xbox One WAY more than PS4 under normal circumstances. Lol.