Man, I'd kill for the BBS search engine to be up and running right now... There's many great discussions in the archives on this exact topic, with links to websites that have diagrams and everything. Since that's not the case, you'll have to settle for my version of the answers to your questions. BTW, you are just hitting the tip of the iceberg of cable discussions. You'll find lots of good posts recently that compare different brands of cable. In other words, balanced or unbalanced isn't your only cable decision. Higher quality cable like the Monster Pro stuff is expensive, but some people say the difference is worth the money. Anyway, that's just FYI... Now onto the question you asked...
You never HAVE to use balanced cables with balanced input and output connections just to make it work, but the connection will be unbalanced if the cables are and it can make a difference in the amount of outside interference and hum you might pick up. If you are using short cable runs then it's no big deal. If you are using cables that are like 20' long or more and running them next to all kinds of electrical lines and equipment, then having balanced connections will cut down on the noise level considerably. TRS stands for Tip Ring Sleave, and means the cable is balanced. Most normal instrument cables (guitar) aren't TRS though, so make sure you have TRS cables and aren't just refering to an unbalanced instrument cable as TRS. (This is where that diagram would come into play nicely

)
You should be able to buy balanced cables from Musician's Friend, search their website if you don't see them in the catalog.
Here's a sample of the HR FAQ on the main HomeRecording.com page that gives some more details on balanced/unbalanced connections.
-----------
Balanced vs. unbalanced is a different matter: -10 is usually unbalanced, +4
is usually balanced. Balanced lines offer excellent immunity from hum and
noise pickup. This is usually the reason a studio is using +4dB because
they want the balanced lines.
An unbalanced line has the "hot" and "ground" wires.
A balanced line contains a "positive" and "negative" (electrically
inverted) copy of the signal (called "hot" and "cold" respectively), plus a
shield ground. The receiving-end of the cable inverts the cold and adds it
to the hot (assume the "value" of the signal is 1:
N = noise pickup in the cable
hot wire + (- cold wire) = 2
(+1 + N) + (- (-1 + N)) = 2
You end up with a double-voltage signal (the doubling is 6dB of gain). Any
noise pick up cancels out neatly.
These are line levels. Mic levels are typically about -50dB, instrument
levels are about -20dB (but they can vary widely).
-----------
[This message has been edited by Jon X (edited 05-20-2000).]