poor mystic, I was lucky in that a young friend (he's about the age of my stepson) visited for a week from across the country last February and wanted to play with some microcontroller stuff. He bought a bunch of stuff from the Microchip website and we taught ourselves the basics during that week.
The two main kits that I recommend from Microchip are: 1) the Low Parts Count Demo board and 2) the PICDEM Lab.
The LPCD is what we spent our time with, as it is the simplest (IIRC, it was around $50 US and was a good value for the money). It has a PIC 16F690 chip (28 pins) on a PC board and comes with the PICkit 2 programmer. You download the MPLAB assembler and tools from the Microchip website and things run on a Windows machine. The board has four LEDs, a pot, and a pushbutton switch plus room for some prototyping. All this stuff would fit in your shirt pocket. There are 12 lessons. The lessons are all in assembly language; normally, I'd rather program in at least C, but in this case learning the assembly is good because it teaches you the chip's architecture. Go through all the lessons, as you'll learn all the basics like analog inputs, digital I/O, interrupts and ISRs, and the mechanics of getting things to build and run. For someone on a budget and not much space, this is what I would recommend. Once you've gone through the tutorials, your mind will race with all the things you can see you can do with that 28 pin chip (get a few extra, as you will want to play). You'll also like the low power features. The data sheet is over 300 pages, so there's a lot to learn.
For around $125, the PICDEM Lab is a better choice for the electrical experimenter. It comes with a prototyping board, a number of sockets for different PIC processors, and an on-board power supply that runs from a wall wart. Also, there are all the wires and components to make up the tutorial circuits (for example, one of the tutorials makes a temperature-controlled oscillator that drives a little speaker using a MOSFET; a thermistor senses the temperature). An advantage of the PICDEM Lab is that you also work in C and the tutorials' documentation is a bit more polished. It comes with the PICkit 3, which is a later model and a bit more capable. However, Microkit rather dumbly left out the neat software app that comes with the PICkit 2 (EEVblog does a justifiable rant on this). I found I prefer to use the PICkit 2 over the 3. Note that you can't do in-circuit debugging with the PICkit 2 without buying a header circuit for the 16F690 (we used the PICkit 3 to do some ICE with a different processor board and it worked fine). For an electrical experimenter, I think the PICDEM Lab is definitely the way to go if you can hork up the bucks.