Private parts or sex organs are the essential parts to be covered. A woman’s chest, additionally, is a private part, that needs to be covered, too. The adjacent parts with the private parts are also covered for better covering. Therefore, from naval to knee must be covered for both male and female bodies. Women should cover the adjacent parts of the chest like the area below the neck, and shoulders.
The more a body is covered the better. We can categorize the level of covering a body as essential, good, better and the best. However, that what is usually stays exposed needs not to cover.
The head is not counted as a private part. However, covering of heads for both men and women has been a cultural norm that is appreciable.
Headcovering during the prayer is one of the manners of prayer, it is not obligatory in the sense that if head is uncovered it will invalidate the prayer of a woman.