That sounds like a fantastic project! Here are my answers to your questions.

1. What is your career choice?
I am a research scientist. Currently, my research project involves studying solar cells.

2. How would I find the starting temperature of the cooler?
To measure the initial temperature of the cooler, use a thermometer or a thermocouple. Make sure you leave the thermometer in the cooler long enough to get a stable measurement. It may take a few minutes before the temperature reading stops fluctuating, depending on the type of instrument you use.

I have several suggestions that will make the comparisons easier.
a. Use the same amount of ice in each cooler. Also make sure the water and salt water start out at about the same temperature before you add them to the ice.
b. Make sure the beverages all start at the same temperature and use the same volume of each beverage.
c. Keep the beverages all in the same type of container, unless you are also interested in seeing how the container affects the beverage temperature. Heat transfers faster through metal cans than glass bottles, for example.
d. You can define how fast the beverage cools in two ways. (1) Which beverage reaches the coldest temperature after a set amount of time or (2) which beverage cools to a set temperature in the least amount of time. You can determine both by measuring the temperature every few minutes so you can create a graph of temperature versus time for each beverage in each different cooler. If possible, I suggest leaving the thermometer or thermocouple in the beverage as it cools for ease of measurement.
e. It may be simpler to start with just one type of soda and one type of milk for your first measurements. With only two beverages, you will still have to do 6 experiments to test all of the cooler conditions. I expect the results will be similar for coke and sprite and for cow milk and goat milk.
f. Overall, try to be as consistent as possible with all of you experimental procedures. Be sure to write down exactly what you do for each experiment so you can repeat the same steps in the next one.

3. What do you think will happen? Why?
I think the cooler with ice will cool the beverages the fastest and I think the milk will be cooled faster than the coke and sprite.

The cooling rate will depend on how rapidly heat can transfer from the beverage to the surrounding material. Heat can transfer by three means: conduction, convection, and radiation. Conduction will occur when heat from the beverage transfers to the surrounding material by the vibrations of the atoms touching each other. Convection will occur as the warmed fluid (either air, water, or salt water) near the beverage moves away and colder fluid moves in. Radiative heat transfer occurs when heat is emitted as electromagnetic radiation, but this mechanism will not be very important for a room temperature beverage. (Radiative heat transfer is more important for hotter substances like white hot metal or stars which emit heat through empty space.)

Because the water will be in better direct contact with the beverage container than the ice, which will have air gaps between it and the beverage container in some places, I expect the water will have better conduction than the ice. Also, since the water is a fluid, convection will help move some of the heat away from the beverage. Therefore, I think both conduction and convection will be more efficient for the ice water than for the ice alone. I expect the salt water will be even more effective than the plain water because in addition to having good heat transfer like water, it will also be colder than the water. This is important because heat flows from hot to cold, and it transfers faster when there is a larger difference in temperature. Salt water freezes at a lower temperature than fresh water so the salt water will melt the ice faster allowing the salt water to get colder faster, and therefore cool the beverages faster. It is important to note that even though the salt water cools faster, at equilibrium (when all of the ice is melted and mixed with the water) the water and salt water will be at about the same temperature (assuming the same starting quantities and temperatures are the same). The difference is that the salt water will melt the ice faster, which makes the water colder faster, which will cool the beverages faster.

I expect the milk will cool faster than the soda because milk has a lower latent heat capacity than water (3.93 J/gK for milk vs. 4.19 J/gK for water), meaning that milk holds less heat than the water. However, the heat transfer depends on the thermal conductivity and density as well as the latent heat capacity of the beverage, so my prediction may be too simplistic. Also, I am not sure how or if the sugar and ions in the soda will change its latent heat capacity.

Please feel free to send additional questions if you are curious about the thermodynamics of heat transfer or have more questions about your experiment.

4. What do you have your credentials in?
I have a Bachelor’s of Science (B.S.) degree in Chemistry and I am currently in a Ph.D. program studying Materials Science and Engineering.

References
specific-heat-fluids