Photoresistors pass a low current, so a 1/4 W resistor is fine. Even 1/10 W is OK.
Photoresistors have a resistance specified when completely dark and when brightly illuminated. If a cell has 10k ohm when brightly lit, and you have a 10k ohm series resistor, then at the connection between the two components your voltage will be half of the voltage you applied to the circuit. As it gets darker and the photoresistor resistance increases, that voltage will change.
It is helpful to pick components that provide as large of a readable change (analog input) as possible.