Reddit reviews Quantitative Equity Portfolio Management: An Active Approach to Portfolio Construction and Management (McGraw-Hill Library of Investment and Finance)

Well, the trick is to do one step at a time. Your goal is a very reasonable one, but you'll want to focus on the foundation first. For a non-programmer, I would recommend starting off with Code Academy or Coursera. The advantage of the second link is that it immediately provides you with a sense of direction while learning a language. Code Academy's Python tutorial is really nice in providing interaction with your code. Regardless, you'll want to first gain a sense of syntax on your language of choice.

After you're familiar with at least one language, the next most important thing is to become familiar with data structures and algorithms. This book on Amazon is amazing for giving beginner advice in the area: http://www.amazon.com/gp/product/1468108867

The book is not overly complex and mathematical compared to many other books, and it provides a fairly reasonable foundation for any beginner. If you ever want to practice writing basic algorithms out (optional), visit Codility's lessons to try things out. Once you can comfortably complete some of their lessons with a high grade and understand their topics, you should be ready to dive into the math/finance side. I feel that at this point, the Max Dama paper is a great way to get an overview of the basics. Regardless of the financial instruments you're trading (I've mainly worked with equities), you'll need a sense of portfolio management. Here's two books that may be worth running through:

http://www.amazon.com/Quantitative-Equity-Portfolio-Management-Construction/dp/0071459391

http://www.amazon.com/Expected-Returns-Investors-Harvesting-Rewards/dp/1119990726

They're both equities based (and I could be wrong here about FX), but it's probably a good idea to get a sense of how to measure returns. Regardless of the asset class you're planning to trade, all algorithms should be rigorously backtested and simulated (traded with virtual money) prior to being moved into production, and one of the best ways to improve your outcome is to know how to measure the returns and risks associated in your backtesting/simulations.

Hope this isn't too much information at once, but it should be a start. The first two courses throw-it-out mentioned in Coursera is a great start too.

Edit: I'd also take some time to browse some of the links on the sidebar in this subreddit. Some of those links are immensely helpful (especially the Statistical Learning one). Many of the strategy links are fairly easy reads and are recommended as well.

I have a similar academic background as you (math / econ) and am a largely self-taught quant. For books, I recommend Active Portfolio Management and Quantitative Equity Portfolio Management. I also recommend academic papers to get a feel for the empirical side in addition to theory that you will read in the books. Great papers to start with are Fama / French (1992) and Avellaneda / Lee (2008). As mentioned, Quantopian is also great for the user forum and pre-baked back-testing engine. You would also find a lot of value in building your own simple back-testing engine in python or matlab or whatever. I wrote mine in python.

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Don't feel intimidated. When I first picked up academic papers, I understood 10% of it on first read. Now, I'm able to breeze through many of them, depending on how esoteric the math / symbology is. Feel free to message me any specific questions you need and I can try to point you in the right direction.