"As I read various forum topics, occasionally someone says that they will have to check their book about a point of style. My question is what book(s) would you recommend to a student dancer? "
This is most commonly a reference to the ISTD technique book for standard or latin, though there are publications by others as well.
These do not really cover "style". They contain very explicit information about some aspects of dance technique which are required to be memorized for teaching examinations, and as a result can provide a useful roadmap for the school figures. But there is also a lot that the technique books leave out, or which can only be found in them once one is versed enough in their language to read between the lines and visualize how to "connect the dots" between the snapshots in the time given in the charts.
The book won't teach you how to dance, but there is a lot to learn by comparing your impression of a figure that you do know to how it is described in the book, and seeking to understand/resolve any discrepancies you find.