I'm going to be honest here; this topic is not useful. It's like asking what the temperature is today on Earth. Too many valid answers.
The basics of electronics are things that high school students could learn. Defining a resistor, capacitor, inductor, crystal, and IC barely gets you in the door. Also, knowing the relationship between power, amperage, voltage, and resistance is basic. Any entry level courses should teach you how to do this.
What you really want is to jump from the basics into fully formed complex projects. It's not going to happen. Before you go any further you've got to understand some very basic things. For that, you're going to want to putter around with some entry level (read: cheap and simple) hardware.
You should have:
Basic Micro-controller: ideally something like an Arduino or Basic stamp
Resistors: Boat load. You'll need various sizes to run LEDs and create tank circuits. They are cheap, so splurge and get a ton of different values. If you can't look at a resistor and tell its value then you've got some reading to do.
Capacitors: Same as resistors. The electrolytic are cheap, though I prefer ceramic for durability. You will have to worry about type later on, but for now buy what you can get your hands on.
LEDs: Your choice here. They make it very easy to figure out if you've turned something on.
Inductors: Skip these for beginners. You're unlikely to need them unless you're doing a radio project. Even then it's easy to wind your own.
Micro-switches: Get a few. The sign that you've got a good understanding of the basics is that you can disconnect the micro-controller from your computer, and have something you can interact with using only what is on it.
Breadboard: Get a ton. Failure is a part of experimentation, and having a chunk of breadboard to reiterate the circuit (without the need to solder) can save your behind.
Perfboard: Once the circuit is done and tested it is time to see if you can solder it. Perfboard is where you use all your dextermity.
Solder/Soldering Iron/Desoldering wick: You'll make mistakes. Make sure to have a good hot iron, enough solder to fit the project (and appropriately sized solder for electronics, not pipe sweating), and enough desoldering tools to cover your mistakes. Mistakes are how you learn, so don't be discouraged.
For the future: Transistors (NPN and PNP are common), Relays (for the really heavy loads), Actuators (solenoids), and Microphones/Speakers. All of these things can let your electronics project interact with us mechanical beings. They'll be hard to understand at first, but eventually you'll be adept at using them.
If you're ambitious start by making a game of Simon. If you're insane, go for pong. Those LEDs can do quite a bit, and paired with the right micro-controller the limits are your imagination and the hardware. I'd recommend Hackaday.com if you want to see some cool projects. Their archives are a great place to find some information, though some of their projects are way out of a beginners league.
EDIT:
I think a relaxation oscillator is way beyond what is being looked at here. The OP hasn't even touched the imaginary domain for tank circuits. A steady state equation is about two steps beyond that.