Sir Steven Runciman, History of the Crusades is authoritative and has withstood the test of many comers. The crusades were the result of creative problem solving by Pope Urban II. He had a letter from the emperor of Byzantium complaining about the attacks of Saladin on his territory and asking for help. French clerics had been trying to cope with the disruption of idle knights who were disturbing the peace and disrupting farming. So, he suggested that the knights go to Constantinople to help the emperor out. He sweetened the proposal with indulgences, but the crusades were not primarily religious.
The first crusade was not well provisioned and as they marched to Asia minor they ate everything in sight, arriving in Constantinople a ragged and hungry mob. Frightened, the emperor sent them on to Jerusalem. A powerful motive was to provide access to the holy places associated with the life of Jesus which Muslims had closed. After conquest, the knights templar were formed to guard these shrines, but the crusader states did not last long. Richard the Lionheart is the biggest hero of this crusade.
Economic and cultural broadening were the main efects of the crusade. As I said, they were not primarily religious, at all. Ironically, a movement that began to help Byzantium eventually sacked Constantinople in 1204.
Actually I don't think Runciman is really very much respected today among crusade historians. The key figures now are Jonathan Riley-Smith and Thomas Madden. Runciman belonged to the old orientalist, Arabist school. No historian today accepts the "crusades vented steam from Western Europe by siphoning off the idle knights" theory because if you look carefully at the people who went on Crusade (and computerized prosographic studies have now been done analyzing just who went), it was not just the idle, younger sons of the nobles but the top-line nobles themselves, those who were on top of the pile, were not champing at the bit to achieve a place in society but had already achieved it. They went, as did younger sons as well.
And I think it fair to say that most historians today emphasize the religious character of the crusades. They were justified responses to religion-inspired warfare and the primary motivation for men "taking up the cross" was in fact religious. I'm sorry, but Runciman really doesn't cut it anymore. He represents that old secular English cultured snobbery in which everything religious had to be reduced to non-religious causes.