One of the Comprehensive exams I am studying for has to do with the Eighteenth Century Enlightenment. The guiding thread of my studies is that religion (and even somewhat orthodox Christianity) was crucial in moving society into a place of toleration for religious dissent. England is the paradigm for such changes (even though the genesis of much of these ideas flow from the interaction of exiles in the Dutch Republic (the place Spinoza hung out).
According to David Sorkin in his excellent recent book The Religious Enlightenment, the movement for toleration was lost to the French especially because dissension was stamped out by the union of monarchy-nobility-Catholic clergy. Therefore, when the Revolution happened in France, the moderate Christian voices were a minority between those clergy loyal to a papal monarchy and the old order and the followers of the philosophes, who distrusted religious beliefs in general. So when the Jacobins took control in about 1793 and the Terror was unleashed (not to mention de-Christianization) many of the moderate voices were lost. After Napoleon was defeated, the reaction toward the French Revolution and the Enlightenment was one of distrust especially in moderate to conservative religious circles.
A popular argument is that the English "Bloodless" Revolution is the paradigm because it is somehow framed as God-based whereas the French Revolution with the Terror is secular and thus violent to its core. This analysis is a little shaky for at least two reasons. One, nobody can question that the Terror was out of control but one can understand after centuries of feudal abuse, in addition to internal fighting in France and external invasion, why it happened the way it did.
Second, to proclaim that the English Revolution was bloodless is simply ridiculous. The "true" Revolution actually happened alongside the Civil War in the 1640s and the rise of Cromwell's army. Nobody would call this fight bloodless (especially when one weighs in on the suppression of the Irish). The Revolution by William/Mary at 1688 was more of a clean-up operation to remove another Catholic king, James II.
One person that I never thought of seeing in the light of these times is John Bunyan (1628-88) author of the Pilgrim's Progress (historians Christopher Hill and Richard Greaves make this point). Bunyan was a soldier during the war and was upset when the Puritans brought back the monarchy in 1660 with the Restoration of Charles II. He was a "people's pastor" who had friends among other dissenting groups. Bunyan himself as a Baptist was also a dissenter and spent 12 years in prison for his beliefs that he had a right and freedom to preach the gospel. One idea from this is to raise the point that here is an orthodox Christian thinker willing to spend time in prison for an Enlightened opinion; his works should then be read for the social-political, and yes, religious implications they had.
All this is to make the point that the Civil War was extremely bloody (but what revolutionary moment isn't) but it was acted out because of political/religious issues. Those issues continued to be debated and fought for by dissenters like Bunyan and John Locke even after the Glorious Revolution in 1688. In short, the Enlightenment in England like France has its foundation in blood and tears but that is sometimes the price society pays for the freedom of conscience.
If I had to define the method that I am most comfortable with, I would probably place myself within the Intellectual History tradition. This tradition has come under fire for being too philosophical or not contextual enough, but I think it has much to offer multiple disciplines. The author I will be leaning on for help to describe this method is Dominick LaCapra. LaCapra is famous for his work on Intellectual History and his work on the Holocaust; some of the questions he raises is on how historians can show empathy for their subjects like in a topic as grave as the Holocaust. Much of the information below is found in Elizabeth Clark's book History, Theory, Text.
LaCapra describes Intellectual History as "a history of the situated uses of language constitutive of significant texts." He criticizes a documentary historiographical approach (this includes both social and economic historians) to texts as positivism; he notes that historical documents are never simply just "there" to read. His point is to ask what do these text really do. Oftentimes the move is to read everything per context or authorial intention and thus the text takes a backseat to the context. However, context itself is something that also needs interpretation. Another factor to take into consideration are those traces in a text of what is actually left unsaid. LaCapra therefore focuses on the place where contexts and texts come into relation with each other. Clark notes that what is so helpful about LaCapra's method is that his concern for language does not compromise the importance of good research practices. Therefore, better reading methods with regards to a more nuanced reading of the context/text and the way the historian actually reads them combined with typical research methods of archival work, and attention to primary and secondary works is the method that seems to form here.