My thoughts are not organizing well today, so this may be a little disjointed. I hope you will understand, since there are many angles from which one might approach the topic.
First, let us consider the wage gap. I am also feeling a bit unmotivated today, so I shall just direct you here to read a thorough yet concise, fact driven, examination of the issue. Having grown up around the supergirls of my generation, I have no doubt that there is no inherent reason women, on average, should be less qualified for any but some of the most physically taxing jobs than men are on average. Thus the fact that there is a gender wage gap seems like a grave injustice.
Although the above article mentions it, I believe it is worth addressing the issue of "women's work." Society normalizes men holding jobs in the public sector while women do domestic work. While this can be disheartening to women desiring traditional jobs, or emasculating to men feeling more comfortable in a domestic role, I think the greatest problem with this state of affairs is the difference in value that these roles receive. An obvious way to recognize this difference is to examine the wages of those in the different roles. Professional domestic workers are not the best compensated laborers, and the difference is even more marked when a women does the domestic work for her own family, usually earning no pay at all.
I think that good goals for a just society are, elimination of statistically significant pay gaps between genders in most professions, elimination of gender based association with the public/private workforce, a more equal valuation of work done in the two sectors (public and private). Due to our cultural conditioning it may seem odd to consider private work valuable, but consider which creates more human pleasure overall, two hours of a stockbroker trading and advising clients, or two hours spent preparing a warm meal for a family. I submit that, were both two be neglected, we would miss the meal more than the stock advice.
As mentioned, I am feeling unmotivated, and now very tired, so I am going to skip my customary editing read through. Please excuse the lack of polish on this, I'll delete this paragraph if I get around to revisions later.