Well, the absolute first thing you need is a breadboard. If you just start soldering things, you'll get very frustrated very fast. A breadboard lets you just plug things in, try them out, and toss out the smoldering parts easily. You can get breadboards (presumably at Digikey), but also at (ugh) Radio Shack, AllElectronics.com, etc.
If you decide to go the 556 route (or just buy a couple 555's for flexibility) then research the circuits and buy the parts to go with that. If you're serious about getting into this, buy a handful of parts:
Resistors: 10ohm, 100ohm, 1kohm, 10kohm, 100kohm, 1Mohm
Capacitors: 1nF, 10nF, 100nF, 1uF, 10uF, 100uF
Inductors: don't get any now
Buy some transistors: 4400 (NPN) and 4402 (PNP) or 3904 and 3906
Diodes: 1N4005 or whatever. If you're desperate enough, you could use the base-emitter junctions of the transistors (groan)
Some LEDs: Whatever trips your trigger.
Buy like a dozen of each-- they're not expensive. Whatever you do, buy at least three of each. This is true, at least as far as I'm concerned, with whatever you buy. The reason is, when you have a problem, you can do a best-out-of-three comparison to tell if it is the component or the circuit that is the problem.
Remember the old saying, "Never go to sea with two chronometers [clocks]. Either take one or three."
Once you get a circuit working, then buy some boards to solder stuff into. Different people have different techniques for doing this, so do some research into that. I prefer boards with 3 or 4 holes-per-pad. Radio Shack (ugh) has some ok small boards for this, but for bigger ones go to Digikey, AllElectronics, etc.
j.