If you want slow LED flash rates, adjustable by switches (or by a
4066/4016 digitally controlled switch), I suggest looking at a 555
oscillator chip. They cost ~$1 at Radio Shack (much cheaper in
quantity at quality places), and you will be able to find good info
about simple circuits in a 555 oscialltor notebook (I think Forest
Mims has one at Radio Shack). You'll have to toy with
resistor/capacitor values OR you can use your head with a little math
to get the right frequencies. Any engineer worth his salt, can make a
555 osciallator... It's in the book, and left up to you to see (I hate
doing ASCII circuit graphics). The 555 can accurately go from a few Hz
to about 500 KHz (I think).

About the Tape Recorder gizmo, you could alter a stereo tape deck to
use one channel as a DATA line (for flashing LED), and one as audio
line (for voice or music). This would eliminate a lot of noise.

The data line is probably most easily done
by some kind of PLL or bandpass filter (using just an op-amp). The 565
chip is a good PLL, and not hard to work with. However if you nothing
about how a PLL works, I suggest you don't try this. Op-Amp
information can also be found in the Forest Mims Radio Shack
info-booklets, and the popular 741 op-amp is a snap to work with.
Setting frequency and bandpass filter values are not so easy, so I
would suggest the 555 method firstmost... I have no idea what this is
going into, so I am really generalizing...

As for manufacturing techniques, if you're only goofing with it, I
suggest you breadboard the thing... No need to solder. Wire-wrap would
be the next, more permanent step. And lastly, soldering/PCB making.
Hope that clears things......