Watts is a measure of power. Power (P) is the product of the voltage (V) over a certain part and the current (I) through it - V*I=P , expressed in Watts.

a 1/2 W can dissipate more power than a 1/4 (twice as much, in fact), meaning it can handle twice the current at the same voltage etc. It does not mean it automatically does this - how much power is dependant on the parts value and the circuit around it, not the parts power rating.

1/4W is fine for practically anything in effects, and has a nice small size. Carbon resistors of the most common size are 1/4W. Metal film resistors (different construction, same function) of the same size usually are 1/2W.

For this project, 1/4W will do so just get what's easiest.