You could easily do some small projects for less than $100.
I really liked this book for the projects and the breakdown that it gives. Pretty straight forward but it does cover the basics quite well. He discusses simple LED stuff, to motors, servos, temperature or other sensors and how to implement them, and up through Ethernet, bluetooth, etc.
https://www.amazon.com/Exploring-Arduino-Techniques-Engineering-Wizardry/dp/1118549368
He has a website that also gives some ideas for what to purchase.
A kit might be a good place to start. It isn't exactly cost effective for parts, but they usually give a few projects that you could follow guides for to get an idea for how it works and then try to tweak them to do something new, but using the project as a base.
the arduino book : http://www.amazon.com/Exploring-Arduino-Techniques-Engineering-Wizardry/dp/1118549368/ref=sr_1_5?s=books&ie=UTF8&qid=1385381714&sr=1-5&keywords=arduino
looks good. It will probably be simpler than non arduino books, while explaining the subjects you want.
For Arduino, I have read only one book, i.e. [Jeremy Blum](u/sciguy14)'s "Exploring Arduino" (Amazon Link) Alongside you can also watch his videos which demonstrate the making and working of many circuits.
For electronics in general, there's a book called "Design and Technology" by James Garrat. It has a chapter on electronics. I don't think that book's available right now (at least not in my country) as it's quite old. You can still find a PDF online or maybe find it in a library.
There's another book which has a great theme based approach for learning. It's called "The Maker's Guide to the Zombie Apocalypse: Defend Your Base with Simple Circuits, Arduino, and Raspberry Pi" (Amazon Link) It's by by Simon Monk. But I think you can keep that gift for Halloween.
I already use Linux Mint on a VM for general use. Would you suggest something like a Linux From Scratch or Gentoo setup to learn more about these things?
Any particular book/resource recommendation? Should I start with the arduino libraries (which I know are training wheels in the professional world) or jump straight to bare metal?
I'm looking at these:
or
You guys are seriously awesome! I started with some of the sites linked and ordered http://www.amazon.com/Exploring-Arduino-Techniques-Engineering-Wizardry/dp/1118549368/ref=pd_sim_147_7?ie=UTF8&refRID=16E7NMTT777T7D3EAVEG and this http://www.amazon.com/gp/product/B00Q2JYOBE?redirect=true&ref_=pd_hud_ysh_orders
The thermal mass of whatever you want to cool means you'll probably just as well off with a low-frequency thermostat.
If you really want to go fancy, you want pulse-width-modulation. I believe the arduino comes with that built in and is available incredibly cheaply. http://www.amazon.com/Exploring-Arduino-Techniques-Engineering-Wizardry/dp/1118549368
If you want to go incredibly cheaply, consider a PIC Microcontroller. You may have to code up the PWM yourself though.
You can PWM an LED too but the chip would likely eat more than a resistor would. If you need the chip for another reason anyway though...
If you're wanting to go mass production, you probably want a dedicated chip.