What is the price at which zakat is calculated for books intended to be distributed to students of knowledge (purchase price, sale price, or price including shipping and storage costs)? And can the zakat payer choose the types of books himself?

It is not permissible to pay Zakat on trade goods from the goods themselves, but rather from their value. It is permissible to give it to a poor, intelligent student of knowledge who finds it difficult to combine seeking knowledge and earning a living. If you are certain of the need of poor students for books, then the books should be valued at their current price. There is no need to give students a choice, but one must be mindful of Allah's watchful eye and try to coordinate with the students by offering them books of moderate price and quality. If they desire them, they should be given to them; otherwise, the default is to pay Zakat in cash, because Allah commanded to give the medium quality of wealth, not the poor quality.