I mean one of these had Wind Waker, Twilight Princess, and a port of Ocarina...

Gamecube is the worst Nintendo console I ever owned. I like many games on Wii U but I hate using the console itself. N64 for an easy answer.

Most N64 games suck ass nowadays, including acclaimed games like Ocarina. GameCube has two of my all time favorites, Pikmin 2 and The Thousand Year Door, so I'll go with it. I also have a soft spot for the Wii U.

I would say Wii U and GameCube are pretty close (if it weren't for so many Wii U games being ported later, I would say Wii U full stop despite my love for the GCN)

I think my realy answer is that the N64 is just easily the worst of these three. As someone who grew up with it, I have a ton of nostalgia for it as well as so many great memories, and I think from a few specific games it could definitely be said that it was the most influential game console. Mario 64 and Ocarina of Time are two of the all time greatest games, and there's a few other good ones like Star Fox. But overall the N64 lineup is just lacking any kind of variety. Outside of a few great games there just isn't much to play on it. My N64 is still in great condition but I rarely ever play it these days. I still play GameCube and Wii U pretty frequently.

Trying to disregard the feelings of nostalgia and looking objectively - I'd have to say GameCube as a whole (which shouldn't be a surprise given my username :P). I still love certain things about the N64 - its local 4 player options on games like Smash, Goldeneye, and this was when a 90's favorite of mine, Rare, was really on the top of their game. 15-20 years ago I probably would have said it's that console. Generally speaking though, its blocky graphics haven't aged well and its library is pretty thin. Its controller is also pretty funky in hindsight. 

Wii U probably didn't deserve the fate of 14 million sold that it got but there's very little redeeming about it in my eyes other than simply being the first HD Nintendo console. It really only has a handful of significant games, especially when looking at exclusives that haven't since ben ported to Switch. The controller and "miiverse" interface were cumbersome to say the least. 

GameCube may have been a weird looking console, but its library was pretty underrated - outside of the mainline Mario and Zelda games which are admittedly weak. It was especially strong when it came to 2nd and certain 3rd party titles. Tales of Symphonia, Metroid Prime series, RE series, F-Zero GX, Eternal Darkness, Monkey Ball, PSO 1 & 2.. not to mention having what I still feel is the best version of Smash Bros. 

N64 is what I have the fondest memories of by far

For me, it's the N64, by far.

Games like Banjo Kazooie, Ocarina of Time, Mario 64, Banjo Tooie, F-Zero X and Starfox 64 are radiant gems that either pushed gaming forward as a medium or elevated their genres to dizzying heights, and with its 3D capabilities it felt like a bold and exciting leap into the future.

It was an amazing porn machine. Suspending your game for hot girls was instantaneous. There was no way Nintendo was ok with it being used like that..

Gamecube is the only one on that list that I like.

The thumbstick on the N64 controller is so bad that it is the only system where I preferred using third party controllers.
The WiiU was unique but the concept was only ever used well in Mario Maker. No other console I have owned go so little play as my WiiU.
Even today, the controller for gamecube is my favorite. I use variants of it both for PC and Switch.

I cannot deny the classic great games released on the N64, but I rather play them on another system.
The WiiU had few great games and non of them is games I want to replay.

The gamecube was the first system me and my brothers bought with our own money. I connect it to great memories that no other system can compete with. I still have it hooked up to my TV. I like the SNES and the PS3 more than the gamecube but it wins easy over the likes of N64 and WiiU.

Depends on how we frame the question. Best console during its lifetime or best console from the point of view of retro gaming today.

During console's lifetime: N64 > GCN > Wii U
As a retro-gaming console in 2020: GCN > N64 > Wii U

If we are asking which was the best console during its active life, then I think that this is clearly the N64. The console was actually quite dominant in North America up until around 1999. In 97/98 it was the console to own if you were a kid in the US or Canada. It had better graphics than the PS1 and Saturn and games like Super Mario 64, Goldeneye, Ocarina of Time were all amazing titles. The N64 was especially dominant with kids but it also had a lot of popularity with adults as well and had a ton of shooters and mature titles in the first part of its life that made it extremely popular with mature gamers. The N64 was extremely innovative and presented us with a whole new way to play games that had never been seen before, it introduced us to force feedback and was really the first console to effectively utilize 4-player multiplayer making the N64 one of the best party machines of all time. Chances are that your best memories with the N64 was playing with friends (Goldeneye, Smash Bros, Mario Kart) and while the Gamecube and Wii U had these experiences also, it just didn't have the novelty that it had on the N64.

To put it in perspective. When I was a kid I was the first person in my class to own an N64 and I was one of the most popular kids for the first year or so because of it. Four years later when I was the first kid in my class to get a Gamecube, most people neither cared and I even got moderately teased because of it. The Gamecube was never popular and was seen as a kiddie console while the N64 was really seen as a hardcore gaming machine for the first part of its life. Now with the Wii U, I was one of the only people I knew who owned one and unlike the Gamecube, most of my adult friends didn't even know what it was or that it existed. Many just thought that it was an add-on for the Wii and really didn't care about it. Therefore, I say that it is N64 > Gamecube > Wii U.

That said, in terms of best retro consoles to play in 2020, my ranking is Gamecube > N64 > Wii U. Gamecube games have definitely aged better than N64 games and if you can do an HDMI mod to the console the graphics are actually still quite impressive (unfortunately, buying the component cables now are way too overpriced and is not worth it). Playing a Gamecube with composite cables is an awful experience, however, and I do not recommend it as the image will be totally washed out and blurry on a modern HD TV. The Gamecube also gives you access to the Game Boy Player which when combined with the 480p that is possible through the component cables/HDMI mod gives you a way to get very impressive image quality playing your GB/GBC/GBA titles. The Gamecube also had some great RPG's that have aged very well: Baten Kaitos, Fire Emblem, Tales of Symphonia, Skies of Arcadia (graphics haven't aged quite as well as the others but the gameplay and story are still incredible). Unfortunately, the prices for these games are getting very unreasonable in 2020 and so RPG gaming on the Gamecube may not be a feasible thing as time goes on if you do not already own these games.

The N64's main drawback are its graphics. They were amazing at the time but have not aged well at all. In 1997 people were blown away just to play games in 3D, it didn't matter that the textures were ultra low-res or that a character's face was a blocky polygon with a triangular pyramid for a nose. In today's world, however, these graphics are not pretty. The Gamecube delivered much more polished 3D graphics that look a lot better by today's standards. That said, if you can see past the poor graphics there are still a lot of great gems to be played on the N64. Some of the later titles like Majora's Mask, World Driver Championship and Pokemon Stadium 2 really look like they could be Gamecube titles and don't even feel like they belong to the same generation as earlier games like Shadows of the Empire, Doom 64 or even Mario 64. I strongly recommend getting the Expansion Pak and playing some of the later N64 titles if you are going to go this route. Games like Paper Mario and Yoshi's Story also look really good since they went for the more stylized graphics and have not aged badly. The N64 has very few RPG's due to the cartridge format but there are a few worth playing: Ogre Battle 64, Paper Mario, Gauntlet Legends, Harvest Moon 64. The N64 also uses composite cables, but there are numerous RGB/HDMI mods that are very easy to perform with basic soldering skills. Unfortunately, the RGB upgrade does not help N64 games anywhere nearly as much as it does for Gamecube games: the games still look horrible for the most part. It is also really too bad that the N64 didn't provide any backwards compatibility with the SNES and NES with it being that last cartridge-based Nintendo console. It could have been an amazing retro gaming machine if it had the ability to play SNES carts the way that the SNES could play NES games.

The Wii U is not a great console for retro gaming and I do not recommend it. The OS does not seem completely stable to me and I have had more than one lock-up occur with my unit to the point where I was afraid that it was bricked. With Nintendo no longer providing updates or support if something happens to it, I really just don't feel comfortable playing it anymore. Frankly, all of its best titles are either on the Switch or are classic games from the earlier consoles anyways, I would rather play older games on older consoles because they are more stable and there is more that you can do when something goes wrong. It also doesn't help that most of the Wii U's best games had online features that are not being supported anymore or are likely to be taken offline sometime in the near future. Games like Super Mario Maker basically have no value anymore on the Wii U once the online support is gone.