Ok, I will try to explain.
Asking if you should shoot in S-Log2 or S-Log3 is like asking if you should record measurements in inches or feet. I say it doesn't matter: just convert everything to meters before you start calculating.
A color space is a way of representing colors using numbers. Different color spaces use different numbers to represent the same colors. Aside from that, color spaces are equivalent.* They can represent the same images and you can translate between them, just like you can convert between inches, feet, and meters.
Your display uses one color space, something similar to BT.709 or sRGB. (I won't go into the differences now) That color space is optimize for just one thing: delivering a video signal to your display efficiently.
Your camera records in a few different color spaces like S-Log2 and S-Log3 that are optimized primarily to record the range of colors that your camera is capable of capturing. These color spaces are also designed to varying degrees to facilitate manual grading for certain target color spaces, which I'll talk more about later.
S-Log3/S-Gamut.Cine and sRGB are different enough from each other that you can't make an accurate translation from one to the other using standard color correction tools like color wheels and curves. But the good news is you don't need to make that translation by hand. Sony has told us exactly how we are supposed to interpret images in the S-Log3/S-Gamut.Cine color space. So it's possible to build a transformation that accurately translates from S-Log3/S-Gamut.Cine to sRGB. That could be a LUT, for example. (Please note that Sony's LC-709 and LC-709A LUTs are not accurate translations. They serve a different purpose.)
But translating from the camera color space to the display color space in a single step has one big problem: neither of those color spaces make it very easy to perform color correction. You almost always need some basic color correction, exposure compensation at least. There are ways of doing it by hand, but they're not so easy, depending on how much correction is required. Say you need to pull the exposure down by one stop. A curve can do that, but the correct curve has a very specific shape, and it's not similar to the curve you'd need to darken the image by two stops, or to brighten the image by a stop.
That's why some new color spaces were created, optimized for color correction. ACEScc is one, and my Logarist color space is another.
Here's the basic workflow: you start with an image in a camera color space like S-Log3/S-Gamut3.Cine. That gets translated to a working color space like ACEScc. You do your color correction in the working color space, and then that gets translated to the output color space. The end result is that you get the colors you want with less effort. It's a lot like using Adobe Camera Raw or Lightroom to process an image before bringing it into Photoshop. Basic color correction operations become trivially easy. An offset slider, for example, does exactly the same thing as the exposure slider in Lightroom.
When you work without color management, you are just pushing and pulling randomly on the numbers until you like what you see on the screen. In a color managed / colorimetric workflow, the numbers stand for colors in a well-defined way at every step of the process, and the ways you manipulate those values correspond to physical and psychological processes.
If you are absolutely determined to work without color management, at least choose a camera color space that is meant to be graded for the type of display you're targeting. Most importantly, if you are targeting standard HD video (web, TV, Blu-ray) that means you shouldn't use S-Gamut3 or S-Gamut3.Cine. S-Gamut3 is for people who are targeting BT.2020 or for people who are using a color managed workflow. S-Gamut3.Cine is for people who are targeting DCI-P3. Neither of these can be accurately translated to sRGB by hand. So Cine EI mode should be turned off, and you should set the color matrix to Standard, Cinema, or F55 709 Like. As for the gamma setting, you have some choices. S-Log3 is an option, but the HyperGammas are going to be much easier to work with. HyperGammas are actually meant to be graded by hand with minimal effort.
* I said that color spaces are equivalent and can represent the same images. It's not quite true, because different color spaces sometimes have different ranges of colors that they can represent. And when the color values are digital, different color spaces have different levels of precision at different points in their ranges. But if we're talking about S-Log2 and S-Log3 on the same camera, these differences are too small to matter.
