Newton's work is not so much characterized by a specific innovation of thought than it is by a unification of many phenomena. All of the things Newton talks about in Principia had been explored by scholars before, but none before Newton put them into a universal framework. This is the point about the apocryphal apple falling out of a tree: that the same laws describe that as describe the orbits of the planets, of comets, of stars.

The places where you see big contrasts between Newton and his contemporaries are his willingness to accept that Gravity is something of an "occult" force — it is action at a distance without any apparent mechanism. This is fairly anti-Cartesian, where you need a real mechanical explanation for why everything works. Newton basically said, look, I don't know why my law of gravitation works, but it seems to work, so I'm just going to postulate a mysterious force called "gravity" and see where it gets me. This was seen as philosophically very dodgy when Principia first came out but eventually people stopped worrying about it. The Wikipedia page on mechanical explanations of gravitation is a nice place to start when thinking about the weirdness of Newton's theory (because it is weird, we are just taught it from a young age these days so it seems quite natural) and how it fits into other theories of gravitation floating around at the time.

(It is not a problem entirely resolved today — whether gravity is a true force or not is one of the unresolved disagreements between relativity and quantum mechanics. Relativity says it is just a curvature in spacetime, quantum mechanics says there should be a hitherto undetected quantum force particle, etc.)

Newton is the end-product of whatever we want to call the "Scientific Revolution" — he wasn't an innovator in terms of philosophical outlook on it, but the inheritor of a lot of innovations that had already happened. This is one reason he was so appreciated and near-deified in his time, as his contributions were readily appreciated by his contemporaries who were already more or less on the same page, methodologically.