Hello Avery,
To elaborate on Rocco's response, for unbuffered PWM the output frequency would be determined by the setting of the TMOD registers, with a trade-off between resolution and maximum frequency. For your case, the TMOD setting would probably be 0x00FF, assuming a linear relationship between the pulse period and the input level value. The update rate for the colour levels will be determined by the timer overflow period.
To set up the TIM channels, each would need to have its "toggle on overflow" bit set, and would clear the output on the occurrence of each output compare. You would need to update the output compare value within the TIM channel ISR, ready for the next output compare event in the next PWM cycle.
Note that if you require output values of zero and 256 (100 percent duty cycle), these conditions will require special handling within the ISR.
A general comment - if you need to control more than one lighting device from the PC, you would need to also allow for a "device address" value in the communications protocol. In this case you might consider a multi-drop RS485 interface for the SCI.
Regards,
Mac