Frankly your settings are not "good". And there is no such thing as a standard exposure.

If you take a picture and it is too dark, you are obviously underexposing the image. Please be aware that our eyes are incredibly capable of adjusting to different lighting, so that what looks like almost the same in brightness is indeed not.

If you use the camera's exposure, it says 1/250sec f4 and iso 6400, so the equivalent exposure for iso 800 would be 1/30 sec. That is -3 stops off from the 1/250 - which is exactly what you see in the picture. 

While rules of thumb often work - in difficult lighting scenarios, especially indoors, you cannot rely on them. Trust the exposure meter of you camera. 

To combat the iso noise, just compensate by adjusting the exposure time accordingly. Then this should no longer be a problem. 

If you have a lens capable of an aperture below f4, this would also help.

For example, a lens with f1.8 would allow for iso 800, 1/160 sec in the same situation. For this reason, photographers who focus on indoor shooting prefer fast lenses.

Last option would be to add more light, by using constant lights or a flash.