SRV1981

The budget is just for the body and not for the body+glass?
1) Used GFX 100S - the video is good enough for vacation and the stills are incredible
2a) C70 - looks nice SOOC, built-in ND's, nearly the perfect camera for a fast turn-around
2b) GFX 100 II (Love mine)
3a) C70 - as before and the raw from it is flexible enough for anything I do
3b) Used Monstro 8K VV - I haven't actually shot with one, but they seem pretty nice and I sometimes consider doing some trade-in toward one - used models are now about 6k for the brain on reputable used sites

Yeah I heard the original question, and I think that while the posts diving into complex grading are fascinating and useful to those of us who do post, I know that getting good color SOOC is a separate question.
One big point about your question is that it doesn't break down by manufacturer. Not all REDs look the same, not all Sonys look the same, etc. I think the Sony FX6 looks fine, but I dislike the FS7. Also, most cameras have different profiles. Sometimes, there is greater  difference between profiles on the same camera, than between normal/natural/standard/default/whatever profiles on many different cameras. And even within a profile, you'll have totally different results based on how many controls you leave on auto (such as WB) and your lens.
SOOC and minimal grading are completely different. SOOC excludes log profiles, for one thing.
There is budget as well. Best SOOC ever? Alexa 35, probably. Under $10k? C500mkII gets my vote. Under $2k? Nikon Z6 is solid. Are you including lenses in your budget? I like the color out of my Canon L 24-105 better than that of my Canon 50 1.8 (tested on Sony A7rII). Though I have also used terrible lenses for specific scenes, specifically to make them less appealing.
If you want a specific answer or even a specific discussion, ask a more specific question because your original question is extremely open ended--which is fine to start with! But it's probably more useful and interesting to narrow the parameters a bit.

For my own stuff, I prefer it to be as 'faithful as possible' to the original scene, within the limits of the tools I've got and the amount of time I'm prepared to spend fiddling with it. I don't care what someone else wants to categorise that as, but I suspect it would come under your 'video' category.
Personally the parts of the production process I find most interesting are being out-and-about recording the content, the basic editing (the clip choice, 'flow' and the cutting) and getting the best out of the ambient sound. Adjusting the image doesn't usually get much more advanced for me than brightness, contrast, saturation and sharpness, unless there's a clip that's particularly 'off' what I think it should look like in the lighting conditions at the time.
But I'm perfectly happy respecting and enjoying other peoples artistic choices, including abstract art (which is inherently non-realistic). But nobody likes every piece of art they view...

You do realize technology matters? You do realize different camera produce differences in image that are pleasing to some and not others? Do you realize the original thread is about what camera you prefer to get the closest to your goal image with minimal work? Are you aware 99% of responses didn’t address that? Should I wear makeup?

You can agree or disagree or bump whatever threads you want - I showed you examples from the real world.
If bumping threads somehow changed reality, I'd bump as many threads as was necessary to make it so that I could get Hollywood level colour from my phone without any work in post.  Hell, I'd create all the accounts and make all the posts myself if it would actually make it so.
I am so vocal about this because what you are asking about is what I desperately want, but that just isn't how it works.
To answer your question directly, no I don't say that the camera doesn't matter at all, but the camera doesn't matter in terms of getting great shots straight-out-of-camera without any work in post, because none of them can do it.  Have you ever seen ungraded Alexa footage?  It looks just like ungraded footage from any other capable camera (S1H, BMPCC, etc).
In fact, you know what...  here's your answer.  The BMPCC 4K.
Here is a comparison between an Alexa and a BMPCC 4K without any grading done in post except the ARRI LUT (and of course the BMPCC4K has had a conversion put onto it to make it match the Alexa).
Juan is a professional film-maker / colourist and this is the real-deal, not a YT LUT bro product.  
If you think that any camera is capable of what you want then the Alexa must be, and as you can see, with that conversion the BMPCC4K can do it too.
This is the product page.
https://juanmelara.com.au/products/bmpcc-4k-to-alexa-powergrade-and-luts
Knock yourself out!

The image I posted with the bad lighting was GH5, shooting LOG, with a standard conversion to 709.
The GH5 is a huge capable camera, the issue was the lighting not the camera.

Sure.
You just have to hope that the world is perfect and doesn't give you mixed lighting.  That every shot you take has the same lighting ratio.  That your camera doesn't have metameric failure as the WB changes to match the lighting changes.  Etc Etc.
Even on completely controlled film sets, colourists still tweak each shot to even them up between angles etc, so even if the world was perfect your results still wouldn't be.

....and if that image doesn't illustrate the problem with lighting, how about this one.
SOOC HLG:

With a basic grade:

These lights all looked white in person!
I sat down, pulled out my camera (GH5 again), looked through the viewfinder and was stunned at the green/magenta mess the camera saw.

More examples of bad lighting.
This was a 709 shot from my GF3, which obviously couldn't auto-WB far enough to compensate (yes, this looked white in person):

My best attempt at grading in post also couldn't compensate well enough:

But the real demonstration is on a project.
Here's a camera test I shot.  These are the images after grading:

They all look pretty straight-forward, but it took a lot of work to get to that.  Here are the shots SOOC:

Note that adjacent shots have considerably different looks - SOOC:

After:

Obviously I've let the flaring lower the contrast on the middle images to a certain extent because otherwise it would look too forced, but the tint of the first image and second ones needed to be evened out as one had the sun in it and the other didn't.
I've shot these tests by the beach many times, using many different cameras (OG BMPCC, BMMCC, GH5, GX85, XC10, GF3, iPhone, GoPro, etc), shooting manually and in auto, in RAW / LOG / 709, etc etc.  All required decent amounts of work in post to even them out and look normal.
It's like anything - the natural look takes the most amount of work and is, in reality, the least natural.
You keep saying you want nice looking images without doing any/much work, but I've been working super hard at this for quite some years now and it's just not possible.  You either get nice looking images with work, or you wave the camera around and you get out what you put in - a film that looks like a dad with a handycam.
The myth that you can buy it was created by equipment manufacturers trying to sell you cameras and LUT bros on YT trying to sell their LUT packs.

Clearly great points. But I think it’s still missing the mark, given that the user in my scenario wants a quick turn around in many lighting conditions outside of our control what sensors currently produce an image you love with minimal effort. 
 
the gx85 image is lovely but also the kids skin looks deathly anemic. Another sensor and processor would.l render that scene differently.  That’s the conversation 

I debated between the two last year and went with the C70.  It's my go-to A camera these days with the R5 as B camera.  Without watching that video, I'd guess that the image on the right is the C70 (more highlight and shadow detail).

I'm sure I posted it back then too. ML Raw is easy on the 5D3 due to dual card slots and its stability.
I'm sure the FX3 and R5C could get close... minus the 14bit color... but they're $3500 cameras and I already own the 5D3. 

I remember this ! it was posted here years ago! I remember trying ML and was blown away how good it looked but how hard it was to use. I think the fx3/r5c can give those looks now. 

And I'd be remiss if I didn't post this video from a British filmmaker named Paul Cook. It was the video that made me buy my 5D3 and install ML Raw on it and never look back. After 7 years, I'm still chasing what he was able to capture in an afternoon...
 

The first few scenes on the train felt like a movie. Loved it! In another thread I bumped from 2015 where folks discussed cameras and color, as is my goal, some commented that as brands have moved to mirrorless they’re chasing resolution and in doing so neglecting color and overall image. Something to the effect that chasing greens versus other colors, has had a negative impact on the way color is rendered and that’s 9 years ago. Worth a review that thread. 
 
I originally curious about modern cameras that produce that movie look in the first video without lighting makeup etc. the skin tones and overall look felt less digital and more movie like. That’s what I was getting at with what brands are trying to achieve that ? What models most of us can purchase today gets us to that. 

When I did the music video for that band a couple of months ago - it was a nightmare, but at the same time had me thinking - this just feels so right and so much what I want to spend my time doing. If only I didn't have to make a living!

Script and partial shortlist written. Ready for action tomorrow night when wife is out, so hopefully no interruptions!

I agree. His Sony work does not respond to me, neither in the edit, premise, lengthyness, choice of focal lengths, camera movement nor framing nor color palette and contrast. @mercer That Sigma 30mm is a thing I had been keeping in my mind. I am a sucker for 28mm on S35. Kendys Canon work was magic, his Sony uploads on his channel are video imo. Besides colour, movement, framing and lensing are not in the same league as his Canon library imho. I can relate to the impact of a camera on freewheeling video essay work. I still hold a G70 in high regard for the mojo it has in HD 24p. The only two pieces I shot with it are still oozing color magic and forced me to design my shots and movements instead of gimbleing through the world rather effortlessly. No effort means no magic in most of the instances.

Whenever I start thinking about the beginning of the DSLR revolution or the Digital Revolution, I take my own advice and go back to look at some old videos that I love from those forgotten cameras.
This first round of films, from Kendy Ty and his t2i, I have linked to countless times, years ago, but I think they could be helpful or relevant to the OP's topic...
If I remember correctly, he used the t2i and the old Sigma 30mm 1.4. I believe he even created his own picture profile, in camera, for his earlier films.
Like so many others, he eventually moved onto a Sony 4K camera, but many people commented they preferred the look from his trusty, old t2i.
If there's a lesson here, it's simple... sometimes less is more. Sometimes the tool that gets the job done and is simple to work with, is better than wading through the minutiae of features and tech finding the best camera.

Didn't know that was in B&W. Thanks for the heads up. I adore B&W, so much so that I've been testing my FP in 4K 8bit mode for the sole purpose of having a smaller set up for a B&W film. 

It’s not just because the B&W makes it ‘arty’.
The script is great, taking what was originally a book, then a French film, then the well known Matt Damon movie and now an 8x near 1 hour episode series.
The acting is great.
The cinematography IMO is superb.
I have zero criticisms of it and that is rare for me.

Instead, people respond to posts that weren't written and proselytize and talk down.  It's pretty pathetic.   

Literally a non-controversial, non-trolling, basic question that you can partake in politely or not. 

Not really, I've asked basic questions for discussion purposes but the elitism and condescension as your post demonstrates is strong here - i'd rather just find a place with more amateur enthusiasts rather than certain folks who think highly of themselves

I highly recommend going to the source if you're interested in going deeper, here are a couple of interviews with Jill on Joker that I found to be fascinating and thought-provoking:
...and this interview with Jill on John Wick and other films where they even talk about specific shots etc:
Lots of info out there if you search and go looking for it 🙂