The Devshirme was specifically aimed the Christian populations in the Sultan's European provinces. Its only purpose was to recruit soldiers for the Janissary and the brighter ones became parts of the administration. Girls were not included.
There was, a slave trade of women for the Harem. The price paid was based on race, age and virginal status. The most common slaves sold for sexual purposes were Circassians (an ethnic group from the Caucuses, largely wiped out by the Russians), Syrians and finally Nubians. The Circassians commanded the highest price and Nubians the lowest. The current British Foreign Secretary Boris Johnson is the descendant of a Circassian slave girl. Boys were also bought for sexual purposes and again European males brought the highest price.
Hi, I just ran across your post. You may find this answer (and in particular, his linked blog post) by /u/mikedash of interest