Thank you for taking the time to reply!
I have some additional questions:
1. For Web proofing how should I proceed? My ViewSonic VP2785-2K monitor, which according to the specs supports 114% Adobe RGB and 154% sRGB, has the option to switch between Adobe RGB and sRGB. Should I use that one directly or leave the monitor always in Adobe RGB, and use the soft proofing in PhotoShop, using Internet Standard RGB profile for proofing? I get different results in both cases - if I switch to sRGB from the monitor menu, brightness is reduced too much and the colors look too dull, so it is almost impossible to compensate that with any additional post-process adjustments to the photo, while if I leave the monitor at Adobe RGB setting, and use PhotoShop soft proofing, colors and brightness are much better, but I am not sure which of the two approaches is closer to a real sRGB-only device, and also, when doing it with the PS soft proofing, there is almost no difference between the original and proofed images looked side by side, which is also strange. My monitor has never been calibrated, since it was bought, and I use the standard ICC profile, which came with the ViewSonic monitor driver, color management is turned on in Windows and that profile is selected as the default for the monitor. If I turn off the color management in Windows, colors look even a tad better, and to achieve the same looking colors with color management turned on, I have to bump a little the saturation and vibrance of the image, shift it slightly toward reds and deepen slightly the blacks. I am still not sure though whether to use monitor's sRGB switch or PS soft proofing with sRGB. Or maybe the third option would be exactly to have the same image open in another application with Windows color management turned off, and to open it also in PS with Windows color management turned on, and that way to try to achieve the look of the non-color managed image?
Additionally, I guess I should leave always Preserve RGB Numbers switch in the custom proofing settings turned off, since when it is turned on, the colors look horrible?
2. For proofing for printing to a specific printer and specific paper, should I have two different profiles for the printer and paper, or I should have one profile, created for the combination of printer and paper? If I am not able to obtain such a combined profile, which would be better to use for soft proofing - the printer profile or the paper profile?