i want to find out about women in the ancient world--their rights, privileges and place in society. what do I search for?
Goodness ... good luck on that.
If you said 'Biblical world', then you'd get a bunch.
Outside of Biblical, the discussions are buried in the inscriptions/papyri books (in Logos) ... everyday Assyrian transactions and Ugarit inscriptions, prophets, gods, The problem is your question ... 'rights' .... 'priviledges' ... 'place' and 'society' ... almost all modern distinctions, though the norm.
The best not-Logos, pricey-ish:
https://www.amazon.com/Companion-Women-Ancient-Blackwell-Companions/dp/1119025540
I'm not sure how best to formulate a search for that, other than to search for the word "women" in proximity to "rights", "privileges", etc.
Articles, books and dictionary entries may be helpful to you, for example,
There are a couple of Mobile Education courses under the title of Women in the Biblical World:
Happy hunting.
Don't know if it fits your requirements but I saw this while browsing the Logos site and thought of this post.
https://www.logos.com/product/54407/essays-on-women-in-earliest-christianity
The regular non-Academic discount price it $64.99
There is also some eye opening stuff on gender roles, marriage practices, divorce, inheritance, dowry, bride price, etc in this:
https://www.logos.com/product/15711/palestine-in-the-time-of-jesus-social-structures-and-social-conflicts
There's some relevant material in Property and the Family in Biblical Law by Raymond Westbrook.