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What do the cathode capacitors and resistors on the preamp tubes do, per se? I know that the resistors limit the gain of that particular triode, but what about the caps? What effect does changing the values have on the tone?

The cathode resistor set the bias and therefor the operating current of the tube. Plate voltage and plate resistor are the other factors and they all interact.
Sound is developed across both the plate resistor and the cathode resistor. The sound across the cathode resistor acts as negative feedback in the stage and reduces gain. It also reduces distortion and increases linearity.
The cathode cap is a bypass cap. It takes the sound around the resistor and increases the stage gain.
Hope this helps. Its the core of 6 weeks of high school electronics.

Check out http://www.aikenamps.com/CommonCathode.htm

--mark

Alright, thanks. That article helped a lot.