good idea. Your amazon + torrent trick is what I used to just finish the books Seeking Wisdom and Poor Charlie's Almanack.
As for intro books, based on the research tactic you've suggested, I've arrived at a set of "cartoon" introductory books. Specific example: http://www.amazon.com/The-Cartoon-Guide-Physics-Series/dp/0062731009
I'm currently considering math to be most foundational... understanding math may help me understand the other topics better.
Are you also on the same mission as I am?
Do you want to learn real physics or popular science physics which are just conceptual (usually just the "big ideas")?
If it's the latter, this thread has you covered.
For real physics/the basics, whatgoodisaroad commented to mention this book: http://www.amazon.com/Cartoon-Guide-Physics-Larry-Gonick/dp/0062731009
I second that. It's fun and easy. I'd start there and then move on to actual textbooks, if you want to learn the details.
This book got me hooked at a young age. There is a large section on electronics. https://www.amazon.com/Cartoon-Guide-Physics/dp/0062731009
It really doesn't matter which specific game, or engine, or style you start with - it's the concepts that are critical, and can be later applied to any framework. What's most important is to manage the learning curve and keep it fun.
Perhaps start with learning to mod existing games - this will require learning small amounts about a wide range of gamedev-related topics. I remember I started programming and gamedev by writing screensavers and similar in qbasic, and tweaking Red Alert's rules.ini..
Also look for simple game engines (there's zillions) and slowly work up to Unity3D or similar full-fledged engines where you have to do more work at the start, but don't run into limitations nearly as rapidly.
With both modding and making games from scratch happening simultaneously, you're basically doing pincer manoeuvre on core gamedev concepts ;)
Kerbal Space Program's old dev blog has some really intriguing insights into how they worked around Unity's limitations while making that monumental game, and there's many other games' dev blogs which are also a fascinating read when searching for concepts and techniques.
Collect (non-school) books or videos on math topics like linear algebra, physics, matrices, calculus, statistics. These math topics are heavily used in gamedev, others not so much.
Books written for schools tend to be horribly boring and so are actually detrimental to building excitement and inspiration in gamedev; instead, look for books that were designed to be fun rather than grinding drudgery.
I had one in my youth called "The Cartoon Guide To Physics" which I thoroughly enjoyed and highly recommend - I suggest you search for similarly engaging and fun books about the other topics, and don't imagine that school can nurture mathematical skill.