It's got to be the Wii.
Back then, Nintendo were the only company actually trying to do something revolutionary with different inputs (motion control, touch screens). With the Wii and the DS, you could rely on Nintendo offering games that were unlike anything on other platforms. It was something of a golden age in gaming for me. The moment Nintendo stopped directly competing in the raw power race was the best decision they ever made.
It helped that the console and remote were slickly designed. I still think the compactness and the clean lines, in the vertical orientation with that blue LED on the disk drive, looks absolutely killer. Alongside the DS Lite, I feel that Nintendo managed to tap into the Apple ethos of making their devices simple yet elegant looking. Combined with the pitch of "anyone can play this thing", it's little wonder they struck serious mainstream gold. I guarantee a lot of the Switch's success now is coming from people who grew up on the Wii.
The Wii was also the perfect secondary device for true gamers™. I remember when Wii60 was the big thing because you could grab both for the price of a PS3 at the time. When people look back on that 2007 period as maybe the best gaming year ever, most of that was down to those two platforms.
Now, in terms of library, I don't think the Wii was actually as strong as the GameCube. There are of course hits like Super Mario Galaxy, Twilight Princess, Metroid Prime 3, Kirby's Epic Yarn, Xenoblade - the list goes on. But you have to look at what the console can do as a whole. It could play all the GameCube games too anyway, since its hardware was basically just a reworked GameCube. All of those 'Dolphin' games just sort of blended together to become this incredible mega library, as if the sixth gen never ended for Nintendo. Then there were all of the retro games added via the Virtual Console - it remains one of the best retro consoles because it can output 240p on a CRT television.
So if you consider it on all those terms, and add in the amazing homebrew support, it's a really insanely strong package. Almost like a modded Vita or a custom firmware PS3.