I don't pay much attention to all this, so take below with a spoonful of pepper
Grip
That's my finger grip above. My notes say:
"Finger Grip, more precise, small mouse"
Interesting both you guys are claw:
"Claw Grip, rare, small mouse"
Grip types article,
Grip styles video.
DPI
I keep mine at 800 since that's what a lot of pro gamers use for my general playstyle, and my FC6 headshot percentage is over 85%. Higher DPI would prob be better for melee and spray n pray styles, where speed and turning are more important than control or accuracy.
Your physical screen size and resolution also factor in. I'm on 42" size and 1080p res, but if I ever go higher on either, then I'll probably need to increase DPI to avoid it taking an age to cross the display.
Sensitivity
Frindis mentions that above in a knowledgeable way. I can add that S can change the effect of a given DPI setting—so eg high DPI with low Sens would be similar to low DPI with high Sens. I've seen it said FPS favors higher DPI + low Sens, but don't remember what playstyle it was for.
What the diff is between those 2 examples, I don't know—my guess would be to set DPI at your most-used level in mouse settings, and then adjust Sens within individual game settings where it's supported.
There's also a thing about matching DPI with the sensitivity of your mouse's movement sensor. I know nothing about that, but heard to try and keep DPI at even multiples of the mouse's—so eg half or double, rather than 2/3 or x3.79
For old games, it may help to keep Windows' sensitivity setting in the middle—I've always kept it there for general mouse use anyway. Modern games won't use that setting.
Other Settings
I disable Mouse Acceleration and Enhance Pointer Precision in Windows, and in Logitech I disable Smooth Scrolling and SmartShift. That keeps things predictable, so muscle memory can do its magic.
But the whole thing is really like the grip—your personal preference is the #1 deciding factor, and as Frindis said, that can even vary by game. So no hard n fast rule