Here's a brightened and sharpened version of the controller's teaser image from their site:
https://i.imgur.com/iIpQzh6.png
So definitely no weirdo wing-shape :(
On the upper end of the spectrum, OEM controllers from Nintendo are generally considered high quality, but in a precise game like Melee there are a couple things that can cause hangups.
The analog stick might not be properly calibrated. The controller reports the position of the analog stick as its x and y coordinates from -1.0 to +1.0 in both axes. Pushing the analog stick all the way to the edge should result in a 1.0, but some controllers instead report a 0.9875. Completely unnoticable for 99.9% of players, but at the highest level it can make a difference. Sometimes fixed by shaving more plastic off of the controller shell, but custom PCBs let you calibrate the stick manually.
"Snap back" is a more common issue. Tilt the stick all the way to the edge, then let go. Ideally, the stick would return to the center, but oftentimes the momentum carries it past the center into the opposite axis, resulting in a small input in the opposite direction. For some techniques this can have bad consequences, such as Falco needing a neutral input to shoot his gun, but a small input in the opposite direction will turn him around and shoot the gun the opposite way. Common fix for this is soldering a small cheap capacitor to the output of the stickbox's horizontal potentiometer, very subtly smoothing out the directional output.
Fancier mods include things like reducing the travel distance of the gamecube controller's large shoulder buttons to allow for quicker inputs or replacing the shoulder Z button with a clickier button.
This youtube video goes over a popular custom PCB that people have started to use in place of OEM, and some of the reasons why it is desirable: https://www.youtube.com/watch?v=RGyQbXGr4Po
If you just want a decent controller, finding a normal Nintendo-made gamecube controller at a used games store or ebay isn't that hard yet. Odds are it'll still be in decent shape.
If you want to buy a custom one, I don't know if I have any great answers for you. It's a pretty grassroots community, so depending where you live, your best option might be to scour facebook/twitter/discord to find your local Melee players and ask for the guy that makes/sells controllers.
Huh what? That's absolutely not true. I just went to https://github.com/spiritualized1997/openFPGA-GB-GBC and followed the instructions: All you have to do is copying files onto a microSD card. Custom tools are not needed. You can skip firmware checks (wcgw).
All my Gameboy ROMs play without any issues so far. Yes, you have to pay attention to put the files in the correct directories, but I wouldn't call that a "disaster".
The only part I would really have to complain about is the folder names, particularly for ROMs. For SNES for example, ROMs are stored at `/Assets/snes/common/rom.smc`, where obviously `common` is an annoying addition to the path.
If you want to use ROMs, just download the pocket updater and let it do all work for you!
All this is generally my experience with the devices. They feel very like my memory of childhood games, much more so than play in emulation. And I love it.
That said, the software ecosystem side of these devices feels like a near total disaster; I think it's a combination of legal concerns around copyright for ROMs, and the company's DNA. The amount of work to play, say Zelda on an Analogue Pocket, is akin to jailbreaking an Android phone, circa 2013. Lots of sdcard downloads, firmware checks, custom software tools, arcane paths through the OS software. I think they could afford to make a cleaner and easier software path.
At any rate, I will order an N64 capable Analogue console as soon as I can - the idea of having an N64/(PS1? Saturn?) device that will last in my house is irresistible.
I'm also very curious to see what they do on controllers - the N64 had a weirdo wing-shaped controller, and using other control layouts for N64 games seems tough to me. Should be fun!