We just moved into a house that has outside patio lights controlled by 3 different light switches. I want to replace one of the light switches with a digital timer. What type of light switch timer do I need? 3 pole? 4 pole? And does it matter which light switch I decide to replace in the circuit?
It matters which one you replace, because that will determine which type of timer you need. One of those switches is going to be the "middle" switch, between the other two circuit-wise. That middle switch is a four-way switch, the two outside switches are three-way switches. You can determine which is which visually is you don't know the circuit layout - the three-ways will have three wires plus a ground, the four-way will have four wires plus a ground attached to each switch.
This is a simplified and idealized example of the circuit you're dealing with: