Studying effects of alcohol on cells
Great idea! It seems that this research has been done before and your hypothesis is correct, but testing a wide variety of alcohols and testing your hypothesis for each one of them would be a great project.

Now, to do this, I would expect you would need to check the growth of the cells after certain periods of time. How would you do this? Well, the best device would be a hemocytometer. It looks like the price varies from 10.00 - 400.00 which is pretty cheap. Of course, there would be mitosis if there is growth during periods of time, which means there would be more cells after certain periods of time.

What cells to choose? I would choose something easy to work with, such as E.coli. It is safe and easy to work with. It needs minimal resources. Here's a link to a simple culture you can probably make at home:

http://makezine.com/projects/how-to-make-bacterial-brothagar/

Later, however, when you get good data, you can use mammalian and human cells to show that the research is relevant to human beings. However, mammalian cells are harder to grow because mammalian cells grow slower than bacteria and fungi and moreover contamination can cause problems. You would also need biosafety cabinets or laminar flow hoods and learn of aseptic and sterile technique.