It is a bit like comparing apples and oranges, and you can probably look up the subjects themselves, but for a first year mathematics student in university here, I would say that
2. Single Variable and Multivariable Calculus
3. Linear Algebra and Abstract Algebra
are subjects that should be taken without question. (I didn't know what "rational trigonometry" is, though. Actually, I would expect 1. to be a high school course, depending on its level.)
I have ordered them according to abstractness, and I suppose something could be said for taking them in this order. Many people (e.g. computer scientists) would justly insist that you also take
4. Discrete Math and Applied Math
but please note that applied mathematics is not necessarily discrete. (It can be, but there are many other kinds of applied mathematics.) Depending on your curriculum, you may benefit from taking 3. and 4. at the same time, but typically neither is a prerequisite for the other, assuming both are introductory.
I am not sufficiently familiar with courses on geometry (let alone non-Euclidean geometry) to be of much help there. In any case, I consider 1-3 core courses and the others somewhat less so. Ultimately, however, there are many interrelationships between some of them that you will come to see in time. (This makes the subjects more rich and beautiful.)
P.S. I see you are online, but your status line suggests differently? In any case, I hope it helps.