The ARRL Handbook was thoroughly updated for the 2010 edition - much better than an old copy and at fifty bucks way cheaper than Art of Electronics, even a used copy. Start with the chapter "Electrical Fundamentals" and go from there. Similarly, "Understanding Basic Electronics" (another ARRL publication - www.arrl.org) has been updated and the "Hands-On Electronics" book contains a lot of simple experiments that explain the theory behind the circuits. Pick up a used EE circuit course book like "Microelectronics" by Millman as deep backup to the introductory texts. If you live in a college town, the used bookstores near campus are good sources of cheap texts no longer being used for courses, but still fine as a workshop reference.
Electronic project books are fun, but often don't explain very much about how the circuits work, so you'll need a supplementary text for that. For basic how-to-build circuits and common electronic construction techniques, try "Circuitbuilding Do-It-Yourself For Dummies". To build up your junk box and learn how stuff goes together, go down to the local thrift store and buy some junk electronic device, then tear it apart. You'll get lots of connectors, parts, hardware, and know-how for pennies.
In the spirit of full disclosure, I am a long-time ARRL member and licensed ham that learned a great deal of electronics through ARRL publications and by building my own gear and accessories.