Unsure what supply voltage to use to calculate resistance

Right now I have a 12V 1000mA wall wart and am in the process of determining the resistors I should buy. My current situation is that I will be using an arduino to prototype and buy the supplies to make an arduino later. I know that the pinouts on the arduino supply 5V so I'm unsure whether to use 12 volts or 5 volts for my voltage supply when calculating the resistor value.

Depends on what you are using the resistors for. If you are driving LEDs directly from Arduino pins, use 5V. If you are using an Arduino pin to control a transistor to switch a bunch of LEDs running on 12V, use 12V.

I'm not sure what the resistors might be for.
Not a voltage divider, I hope.
Use a regulator or DC-DC converter.

The project is for a word clock and the schematic requires a shift register to be used along with a driver ic. The driver ic output pins are attached to a current limiting resistor and then an led.

"A shift register", "a driver ic" and "an LED"
Feel free to provide any relevant details.

spyrosj:
The project is for a word clock and the schematic requires a shift register to be used along with a driver ic. The driver ic output pins are attached to a current limiting resistor and then an led.

If the 'driver IC' has 5V outputs, calculate based on 5V. If the 'driver IC' has 12V outputs, calculate based on 12V.