What is the difference between lineage (hasab) and ancestry (nasab), and how do we reconcile the prohibition against boasting about one's lineage with the command to choose a spouse of good lineage?

There is no contradiction between the hadiths. The hadith (definition) of Abu Malik Al-Ash'ari concerning boasting about lineage and disparaging ancestry refers to arrogance and showing off to others, not the lineage sought in marriage. The hadith of Abu Hurairah regarding choosing a wife for her lineage means lineage devoid of arrogance, which is what is intended when choosing a righteous wife. As for the hadith, "Choose well for your sperm, for the root has a strong pull," it is weak. Even if it were authentic, it would mean choosing a good origin for the sake of good morals and chastity. This meaning is supported by what Ibn Majah narrated from Aisha: "Choose well for your sperm, marry those who are compatible, and give your women in marriage to them." In summary, the choice in marriage is based on religion and character.