Questions:
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I am hoping to learn and start repairing things like computer monitors
and work up to repairing motherboards, flat-screen monitors (LDC /
plasma and related technology), overhead projectors and maybe even
digital camcorders. -Am I being overly ambitious?

I'd say you are more misguided than overly abitious. It is very difficult
to make a buck repairing commodity items these days. Mostly, they are not
designed for repair but for small size and low cost. They use printed
circuit boards with surface mount components ... the desoldering/resoldering
process requires special equipment and special skills. It also requires
schematics and parts that are difficult or impossible to get.

With my target being learning to repair the above types of devices,
what kind of test equipment would I need to invest in?

Please offer your advice on equipment I may be missing in my list and
also which signal generator and oscilloscope would be the best fit. Old
technology would be fine. Reliable devices I could learn to repair
myself would be ideal. I suppose parts being available for these
devices would be important as well.

Digital multimeeter and a few VOMs (do I need special probes?)
Perhaps a signal generator
Oscilloscope (which probes?) (what kind of bandwidth and sampling
would be needed?)
Soldering station


I am thinking of watching ebay and building my test bench as
inexpensively as I can preferably with reliable older equipment I can
repair or calibrate myself and learn at the same time. - Again, I am so
new to the trade as to not know if what I am saying is achievable or if
I am saying something that would make the seasoned technician laugh!

You are perhaps a potential hobbyist? Again, this is not the right time to
get into the electronic repair business for generating any significant
income. Your equipment list should include an adjustable dc power supply,
if your aim is hobbyist.