There wasn't really a "going rate", in great part because the purpose of a dowry was not to be a "price".
In the early Middle Ages, it was common for husbands to pay a brideprice to his wife's family, a much more direct transaction. The husband and father would negotiate the woman's value, what the husband owed to her family for the right to take her into his. Around 1100, European aristocracy shifted to instead having the wife's family settle a dowry on her instead, usually roughly the amount that she would have inherited if she had been single when her father died, which would become her dower (money/property she was entitled to inherit back when her husband died). This was interpreted by late twentieth century historians like Georges Duby as a decline in the position of women - in the brideprice/bridewealth system, they were valuable commodities that prospective husbands had to lay out substantial money/property for and people who would inherit some of their husband's property after death, while a dowry was said to be a way to buy daughters out of the family property and prevent them from actually inheriting, protecting the family property for eldest sons - alongside a general silencing in politics and aristocratic business. However, this is a rather simplistic way of looking at women's status, and in the early twenty-first century there has been pushback. In "Women and Power through the Family Revisited" in Gendering the Master Narrative: Women and Power in the Middle Ages (2003), for instance, Jo Ann McNamara notes that after this point, aristocratic women continued to exert power in much the same way they always had, arranging marriages and conveyances, endowing abbeys, etc. We can also construe the dowry as a way to literally raise the value of women to their husbands and ensure that they retained a certain amount of property as widows.
By the nineteenth century, this system was still in place for elite women. (Non-elites considered it outmoded and primitive, a form of buying and selling men and women.) However, rather than an actual gift of a dowry, women were more likely to have money and property settled on them at the time of their marriage as a promised inheritance, attached in the same legal document to the amount of money that they would inherit from their husbands when they were widowed, and the inheritances of their children.
It was important for a family attempting to move up socially to put as much of their resources as possible into a daughter's dowry. Joan Perkin, in Women and Marriage in Nineteenth-Century England (2002), states that in the early nineteenth century, a very wealthy young lady from a trade family that was marrying into the nobility or a lady from the lower aristocracy marrying into the higher ranks would probably need to have £50,000-60,000 settled on her in order to make it worth the higher-ranking family's while to take a wife with such a lower position in society. Equals, however, could make do with £10,000-30,000. From this, they would be promised 5-10% per year as an income when widowed.
At lower levels of society, while people no longer referred to dowries per se, it was still frequently important for the woman to bring money to the marriage. Working-class women typically worked in factories or domestic service prior to marriage to save up some cash for setting up an establishment with her new husband (the need for which often prolonged engagements), and both working- and middle-class women prepared trousseaux in order to have household linens and goods once they moved away from home.