TL;DR: Learn by reading, doing, following online courses. Join groups/clubs. Work on projects. Find the area you really enjoy. Eventually you'll contribute to helping people out especially if you believe in whatever field you end up joining.
I love your awesome attitude about math and I wish there were more people like you. Well, there is a lot you can do to help people with math. A LOT! It really boils down to what do you want the world to be like and help it be more like that.
Do you want a greener/cleaner world? Go into environmental engineering.
Do you want a healthier world? Go into the biomedical sector.
Do you want a more technological advanced world? Go into computer science or some technology related engineering field.
Do you want people to be more educated? Go into teaching.
Do you want to do either of these or more but the current environment won't let you? Start a startup company.
I could go on and on and on with these recommendations. The thing is that mathematics is a very flexible subject. You can do with it whatever you want. Heck, there are even Simpsons and Futurama writers who are mathematicians: http://en.wikipedia.org/wiki/Jeff_Westbrook
Don't worry too much about helping people out. It kinda comes as a side effect of doing math. For example, studying graph theory back in the days of Euler may have sounded niche and a waste of time but if it were not for graph theory, no internet. (and certainly no facebook... although... i know people who think that wouldn't be such a bad thing)
Focus on finding something you really like and just roll with it. My recommendation... read, read, read. If you have difficulties taking those courses, read the books. A trick I used to do is that I looked at the syllabi of the courses I wish I could take and just got the textbooks and went through them chapter by chapter.
Learn as much as you can: set theory, graph theory, game theory, optimization, cryptography, differential equations, algebra... whatever you can. And try not to limit yourself to mathematics. We live in a complex interconnected world. Many ideas in math today come from economics and biology and physics and all sorts of places.
When you say you'd like something like taking classes... you know, there just isn't enough time and it is not always possible. But youtube exists. And all those MOOCs (Massive Online Open Courses) like Coursera, EDX, or Udacity. They have loads of courses, some more mathy than others. Even all those computer science Udacity courses are interesting because computer science in the end is all about math.
But learning is not enough, actually working on projects is way more helpful. If you have access to clubs or can get friends to work on some project, you'll learn so much more. Just a simple project like getting a little robot to follow a line on the floor or making a video game will challenge you mathematically and thus you'll get to see how you can apply math in the real world.
So, don't worry too much. Just by your attitude I can tell that you'll manage to do good in the world with math. Just learn, practice, and make awesome.
It seems that you are looking for mathematics that is not too technical. In this regard, I do recommend the textbook 'Comprehensive Mathematics for Computer Scientists' because it contains the type of theory that forms the foundations of mathematics - i.e. sets and logic - without going into numerical analysis. Logic and set theory can be intuitive and fun and is definitely useful for application in other subjects such as computer science and philosophy.
On the other hand, theoretical mathematics that is abstracted from numbers, such as linear algebra (chapters 20 -25), can be difficult to master if you are not dedicated, as there are many complicated concepts to understand. For a student with no math foundation, many of the chapters in this textbook will be fast-paced.
If you are looking to "reintroduce basic maths", then this book is not suitable. A better textbook would be one that is aimed at high-school students or a first-year introductory course. The level of math that you will be at once you have mastered the book will be about the end of a second-year pure maths course at university. You can expect to require 5 hours per week for a year $\approx$ 250 hours in total.
An alternate solution, which is a "self-contained" book and requiring "minimal to no previous mathematical background" is to find a descriptive coffee-table style book on mathematics, such as 50 mathematical ideas you really need to know by Tony Crilly (London: Quercus). In my opinion, the more description that the book gives and the fewer formulae, the easier it is to understand what is going on. This book can easily be read by dipping into and out of different chapters, which each take about half an hour to read and understand (there are 50 chapters).
Best Answer
For a list of great books, see The Mathematics Autodidact’s Aid.