Are all the hadiths mentioned in Al-Mundhiri’s book "At-Targhib wal-Tarhib" authentic, and what are the most famous authentic hadith books recommended for reading?

The book "At-Targhib wa At-Tarhib" by Al-Mundhiri is one of the greatest hadith books that encourages virtues and discourages vices. Its author did not stipulate authenticity for all its hadiths, and he clarified his methodology in the introduction. Sheikh Al-Albani classified its hadiths into authentic and weak. As for other beneficial books for the student of knowledge, they are: "Riyadh As-Salihin" and "Al-Adhkar" by An-Nawawi, "Az-Zuhd" by Ibn Al-Mubarak, "Bulugh Al-Maram" by Ibn Hajar, or the two Sahihs, "Sahih Al-Bukhari" and "Sahih Muslim."