Are there different qualities or types of caffeine?  Does the body
handle caffeine from a quality product (say a high quality coffee)
differently than it handles caffeine ingested through a low quality
product (say a very cheap, low quality chocolate bar)?  Does the body
react differently or handle differently the caffeine ingested
depending on what food/beverage it's ingested with (e.g., regular or
diet soda, coffee, tea, chocolate, etc.)?

Excellent article at http://coffeefaq.com/caffaq.html#Chemically that
answers most of your questions.

In general, the answers are "no."  Caffeine is caffeine (C8H10N4O2),
and the body does not know if you are getting it from a Starbucks
latte, a chocolate bar, or a Mountain Dew.  Of course, it is possible
for caffeine, like any drug, to contain impurities that may affect the
body's absorption of the chemical, but other than that, it's pretty
much the same.

While caffeine is caffeine is caffeine, you may notice some different
effects due to compounds other than caffeine.  Chocolate contains a
chemically related compound called theobromine, which, while less
potent a stimulant than caffeine, is present in larger amounts.  It's
effects on the body are also qualitatively different.  Amounts of this
present may vary more widely than the caffeine, so for something with
equal  amounts of caffeine, you may get more or less effect from
theobromine.  Tea can contain another related compound, theophylline,
in small amounts.  This compound has been used to treat asthma, though
it is becoming less used, but again, it can have similar effects and
varying levels.

Also, when you see statements that coffee or tea or chocolate contain
X amount of caffeine, this is an average or estimate.  Depending on
the type of coffee or tea and how it is processed, this can vary quite
a bit.  Darker roasted coffee actually contains less caffeine than
lighter roasts.  (That may be why "Breakfast blends" tend to be
lighter - more caffeine, not just milder taste)  Likewise, stronger
brewed coffees will contain more than weaker coffees brewed from the
same beans.