It makes no difference, the resistor value (how many ohms) makes a circuit work.

For Arduino circuits you would need resistors of 100 ohm to 1 Mega ohm. Resistors of 1W are mostly up to a few kilo Ohm, so I doubt if you have a good set of different resistor values.

There are boxes with metal-film resistors with all kind of values. They are not expensive.

Suppose you have a led of 20mA connected to a Arduino pin.

Assume it is a red led with a voltage drop of 1.5V.

The resistor you would need is (5V - 1.5V) / 20mA = 175 ohm.

Lets use a resistor of 180 ohm.

The power consumed by the resistor is 3.5V /180 ohm * 3.5V = 68mW.

The resistor would heat up with 68 milli Watt.

So a resistor of 100mW would be okay.

Using a resistor of 1W doesn't make a difference, but it also makes no sense to use such a big resistor.