Right now I'm a few periods before getting to actually specialize in anything, but so far I'm way more into algebra and logic than analysis or geometry.
Topology is interesting too, and it has lots of algebra.
The thing with Newton's Principia is that before of them pretty much every serious scientific study was faith-biased or plain discarded. Without Galileo and Kepler, however, there would be no Newton.
Newton does start real physics and thus a rigourous study of the universe, and also "invented" calculus (some of his ideas weren't new, from Pithagoras to Fermat, there was a "basic" idea of it; and there's the Leibniz dilemma) in order to help with the calculations, but it's more about physics than it's about math.
Math is what the physicists use to study the behavior of a system, and both disciplines have influenced each other heavily, altough for me, math is more than reality modeling, there's creation and proofing of things wich may or not exist. "Quoting" G. Hardy, there are two kind of math: "pure" math, which has nothing to do with reality, and "real" math, which can be used for something. The true geniouses, according to him, cared not about reality but about the consistency and correctness (and therefore the invention) of theorems and ideas.
I'm more into "pure" than "real" math.