Newton's ideas were certainly existed within a tradition that was a lot bigger than him. You can trace the ancestry of Newton's thought backwards, through Christiaan Huygens, Rene Descartes, Galileo, Niccoli Tartaglia (among many many others), and from there you have to go to the medieval impetus theory of motion, as well as the works of important Ancients like Archimedes (and those who followed him), whose works were rediscovered in the 15th and 16th century. I don't think the reformation had much to do with the development of Newton's thought, because the Catholic Church tolerated plenty of changes to its philosophy (e.g. the change from Aristotelian philosophy being banned by the Church in Paris in the 11th and 12th centuries, to becoming the de facto official doctrine of the church by the 14th century), and in any case most of the people who Newton was most indebted to were Catholics. The fact that Galileo got into such hot water with the church was an unusual event and should not be taken as emblematic of the Church's relationship to science. Exactly why the Church got so hung up on Copernicanism is an interesting issue, but I'm not going to go into it here.

Anyway, Newton's ideas, particularly those on motion, had a long tradition. Newton's three laws of motion for example weren't all his own idea. The first law of motion had previously been stated by Galileo, the second was an idea that had previously been proposed, although not in the form that Newton gave it, and the third law was Newton's own.

What really made Newton special were two things. Firstly, he was the greatest mathematician of his age. The man was simply a genius, he could manipulate mathematics in ways that people didn't even think of before. The Principia, Newton's major work, was so difficult to read that Edmund Halley asked him for a simplified version because he couldn't get through the whole book. That's Halley of Halley's comet; this guy was no idiot. In fact, it has been suggested that Newton deliberately made the book harder than it needed to be (Newton is also known for not being a very pleasant man).

Secondly, Newton spent the first 15 years of his career investigating alchemy. When he came back to work on motion and astronomy, he brought back some ideas with him from his work in alchemy, specifically ideas about force. The dominant trend in the study of motion prior to Newton was called the Mechanical Philosophy, which stated that the world fundamentally acted like a machine, i.e. that all phenomena can be explained by bodies in motion hitting each other. There was no action at a distance. Newton's introduction of force into the study of motion helped to quantify the field, but what was really novel about Newton's theories were that they proposed the existence of a non-contact force: gravity. Much of the work of scientists in the previous 50 years had been an attempt to get rid of spooky things like "faculties" and "powers", which had been the way the study of nature had previously been conducted. Something would put you to sleep if it had a "sleep inducing virtue", which had been criticised as simply a fancy way of saying "this herb will put you to sleep because it has the power to put you to sleep", which of course says nothing at all. So Newton's reintroduction of things like force to the study of motion made a lot of people very uncomfortable.

Newton was aware of the fact that he hadn't explained what gravity was, he had simply quantified it. He wrote the famous phrase "Hypotheses non fingo" "I feign no hypotheses" about what the cause of gravity really was. Eventually Newton's theories won out not because of their explanatory power, but because they were just so good at predicting the results of a huge variety of phenomena.

It's pretty dated now but I recommend Richard Westfall's biography of Newton, Never at Rest (1980). It gives a good overview of Newton's life as well as how and why he came to believe the things he did.