Which are the criteria I have to follow to choose a citation style for my book?
I assume you are asking about an academic book, in which case the following applies:


If the publisher's style guidelines specify what citation style to use (many do), then use that one.
Otherwise, use the citation style that is commonly used in your field. Here is a list of the commonly used citation styles for many fields.
Finally, if several styles are commonly used in your field and the publisher has no requirements, choose the one that you think will be most useful to the reader. (For example, depending on the content and style of your book, you may find footnote citations more useful than in-text citations, or vice versa.)