The display profile you use in DT should be the calibration specific to your monitor. sRGB is only a good choice there if your monitors gamut perfectly matches sRGB - which is unlikely.
The safe output profile for web is sRGB, because most monitors can display it. I have a wide gamut monitor and still output sRGB for web. The other profiles tend to have niche uses. For instance, if you know your specific audience on the web has wide gamut monitors, then it is safe to output that way. Or if your work is intended for a display with DCI-P3, then output that way. Or if you printer is wide gamut and you print a lot, etc…