You may not come from the same culture that I came from, but the early significant milestones in my mathematical education were:
1. Reading the "aha!" books by Martin Gardner, as a child.
2. Reading Lockhart's "A Mathematician's Lament" [1]
3. Linear algebra, calculus, and complex analysis classes. I was taught
these at Cornell; you might look for them via MIT's OpenCourseWare [2].
4. A bunch of combinatorics, from Cornell's classes in probability.
The most key thing I can tell you about mathematics is, always go back and read the definitions. Always. I have sometimes helped out math students on topics which were way out of my depth, simply because I picked up their textbooks, flipped several pages back, and said "hm, what does this word mean? what does that word mean?", building up connections all the while.
You may also want to start in a completely different direction, since you're interested more in CS-based topics (I am interested more in physics-based topics) by starting with number theory and modular arithmetic, and of course MIT has a Comp Sci section [3] which also produces lectures on OpenCourseWare; you may wish to watch those lectures.
FYI, Lockhart has a new book coming[1] out with the kinds of things we should be doing, which is something I (and probably everyone who read & liked his Lament) have been pining for. I'm waiting like everyone else, so I can't explicitly recommend it. But I certainly anticipate a mental treat.
You may also want to start in a completely different direction, since you're interested more in CS-based topics (I am interested more in physics-based topics) by starting with number theory and modular arithmetic, and of course MIT has a Comp Sci section [3] which also produces lectures on OpenCourseWare; you may wish to watch those lectures.
[1] http://www.maa.org/devlin/LockhartsLament.pdf
[2] http://ocw.mit.edu/courses/mathematics/
[3] http://ocw.mit.edu/courses/electrical-engineering-and-comput...