Color management, customization, what to choose?

Question

Adobe

Good evening!
I ran into a problem, after updating ps all settings were lost. I restored everything, though there were problems with the color "I just forgot what's what" And now I don't know what to choose for processing the photo.
Screen 1
Screen 2

If I understand correctly, then if I just want to post a photo on the Internet, I need to select the 1st screen.
If I want to print it with the same color reproduction, should I choose the 2nd screen?
It used to be something like this: I photograph "nikon d750, if it's important" I uploaded the received photos to the computer. further post-processing in lightroom "there, by the way, now the same garbage comes out"

And what I wanted to process in more detail, already in Photoshop. By simply dragging the desired photos, they open and the profile is automatically selected. After processing, I saved. in psd and jpg. Those that I wanted to put in VK, for example, I prepared for the web (reducing the size, sharpening), etc.
I would be very grateful for the article or where to dig?
What I found, apparently newbies wrote.
If memory serves, then you must select

This to upload to the Internet. It looks like a natural color.
And for a more advanced color reproduction

And if you print something CMYK there.
It seems that you can work in any other profile, after converting it to the desired one.
I didn’t do anything like that, so most likely I’m wrong and I wrote some kind of nonsense.
Theory...
Thank you

Answer 1

#1 is better in any case, just choose the perceptual conversion method, and as Egor Padalka said, just don’t go there until you figure it out) Here is a relatively short and very, very sensible article, chewing everything from the very beginning, and with settings for graphic editors:
https://cloud.mail.ru/public/3e74/jyufmZ9x3

Answer 2

Liquidos , why is that?
Original (screenshot from the monitor)
How did you advise why the quality has deteriorated?
If saturation is selected, then the color tone is more or less similar to the original.
settings
The color of the photo in Photoshop is one, after saving it is another, but if you take a screenshot from the screen, everything is as I see it, what's the problem? This was not there before the update.

Answer 3

sRGB only because all packages use this profile.
Adobe RGB 1998 is as old as the world and let's say it's not niche in cinema 4d, I would highly recommend not to use it!