I am working on a science fair project. My question is if electricity moves better through a thin wire or a thicker wire. I need to collect data and make charts, and the thing I want to measure is the brightness. The only problem is that I'm not sure how to scientifically measure the brightness of a light bulb. Probably not important to the question but it'll be connected to a single D battery.
Because light is a form of radiation emitted by a source, it follows the inverse square law, where luminous intensity decreases with distance from the source of light.
To ensure consistent and valid results for your experiment you will need to ensure the light meter sensor is placed at exactly the same distance from the light source for every reading.
Additionally, to ensure your results are not affected by other sources of light it would be best to place the light bulb & light meter inside a light proof box, which has black internal walls.
While an incandescent bulb can be a good visual indicator of the current and/or voltage in a circuit measuring its brightness and then converting that to numerical data is a very roundabout and error prone method.
There is also a more fundamental problem that you are assuming a relationship between light level and wire thickness which you haven't proved ie your experiment has too many unknown variables.
You would be much better of using a voltmeter or ammeter to measure either the current through the circuit or the voltage drop along a length of wire.
The other alternative is just to use comparative data eg just record whether bulb A or bulb B looks brighter for each experiment.
The only possible reason for using a bulb is to keep the experiment simple using a light meter to indirectly measure current rather defeats that object.
If you want to investigate the relationship between current, voltage and light intensity then that is a perfect valid (and arguably more interesting) experiment but you need to frame your terms to reflect that.
A photo resistor or solar panel make for pretty easy/low cost light measuring solutions, but they are not super accurate and will be much more complicated than the primary project. Hook the solar panel directly to a volt meter. It will measure the amount of green light but will not be linear. For the photo resistor hook a battery in series with it and the volt meter. It will likely not be linear either; but I doubt you need too much accuracy here. If you do, you will have to get a calibrated light meter like Fred suggested.
Though measuring the light intensity is possible, I would recommend just using a volt meter and/or amp meter directly like Chris Johns suggested to keep your project simple.
Alternatively, for a more extendable hands-on measurement you could put a known resistor on each circuit and put each in a known volume of water containing a simple thermometer. The circuit with the larger diameter wire will have less resistance and deliver more power to the equal sized resistor and the temperature of the water would increase quicker. Then with some simple calorimetry math you can calculate the resistance of each wire.
Your question was "whether electricity moves better through a thin wire or a thicker wire"
Power is lost due to resistance. Copper wire has a very low resistance and for your experiment a thicker wire and a thinner wire will perform the same. In other words the difference would be so small that it would be very difficult to measure.
Wires made from other materials, such as Nichrome have high resistance and if Nichrome was used for your experiment, you would be able to measure the difference, as seen by the brightness of the bulb.
Measuring brightness can be achieved in many ways, but generally some sensor that is sensitive to light energy will be required. A web search for "light sensors" will uncover lots of information.