Most effective order for learning different branches of mathematics. So, I'm just a current student with a lot of interest in mathematics. Usually I am on the site looking at the questions and most of them are about things I can't currently comprehend. As I would like to increase my knowledge of mathematics, I like to search stuff up, but often don't know where to start with a subject and quickly get lost in a wide array of topics and subjects. 
The question is this:

What is the best or most useful order for learning different topics in mathematics, both in learning new material, as well as understanding more advanced stuff about old material? Also arranged in a way that seemingly builds off each other to complete understanding of the topics being learnt?

So far I've just covered the basic-general stuff in calculus. i.e. Derivatives, Integrals, Taylor Series, Multi-variable Calculus, Coordinate Systems and Linear Separable Differential Equations.

Note: In order to help narrow the focus, let's use the fact that I am an engineering student, so I would like to learn more about topics in the physics and mathematical applications in the hard sciences, so specifically the fields of calculus, algebra, differential equations, numerical and complex analysis and possible links to physics.

What next?
 A: You have several directions you can go here.   
A.  You will of course  have to go on to more topics.  The reason linear algebra is a good next choice is that it sits right on the intersection of so many different branches of mathematics, such as multivariate calculus, differential equations, numerical methods, and of course algebra and geometry.  It's just impossible to move forward in more advanced math without it, because so much is dependent on both the fundamental concepts and the mathematical methods.  Or as one student put it, "you cannot escape it".
B.  Before suggesting other topics to proceed with, let me offer the idea of "backfilling" your present knowledge of calculus.  The way calc is usually taught is what I call the "splat" method, wherein you are splattered with far too many topics, but provided no depth.  Some of these are fundamental and essential; some are interesting, cute or helpful in special circumstances; and sadly some of them are just plain wrong.  It is very rare that an effort is made to provide perspective by, say, categorizing the topics (let alone spending more time on what is important and skipping some of the other stuff).  As a result, people tend to have a fuzzy view of the subject until something happens to improve their focus; such as they start getting creamed in advanced calculus; or they have to teach it.  
What you need is some way of pulling things together so you have a clear viewpoint on the subjec as well as filling in anything important that you didn't quite understand.  You might find some help with this in a book called "Second Year First Year Calculus" which has some good material.  Or you might look around to see if you can teach a calc course somewhere or at least tutor.
C.  Which topics you proceed with depends to a large extent on your interests, which may or may not be well defined at this point.  But to offer some examples:
If you are interested in physics and mathematical applications to the hard sciences, you will want to take more calculus, differential equations, numerical analysis, complex analysis if offered, and by all means some physics, where you will get to use this material.
If you are interested in applications of mathematics in the life sciences, social sciences and business, you want to look at courses in statistics and modelling.
You can try out abstract algebra and topology and see if they resonate with you.
If you don't know the answers to this, then try several things and see what grabs you. 
D.  Finally, regarding looking stuff up and digressing all over the place, it is really easy to do.  But it might be best to pick one or two specific topics and start with an introduction.  For example, you can decide you will study Fourier Series, or line integrals.  Start at the beginning, and give yourself some grounding. Find a tutorial or acquire a textbook. Work a bunch of problems. 
It great that you have wide ranging interests, but probably would be helpful if you line them up one at a time.  You don't have to get it all done immediately.  There is life even after graduation, and plenty of time to get to whatever interests you; and/or to roam around in different areas of math (some of the best mathematicians do exactly that).
A: Linear algebra is next.  Let me know if you need some books.
