What is the best way to understand the crusades: as economic opportunities; a redirection of internecine, divisive intra-European conflicts; a clash between two different civilizations; or something else entirely?

You could say that they were a clash between two different civilizations. They were first declared by the Pope who stated that the Holy Land must be taken away from the Turks who were Muslims because it belongs to Christians. It was a clash of Christianity versus Islam and many of the Catholic countries sent their armies to fight in the crusades for this reason.