This term is used for experiments where DNA is artificially altered, and then put back in an organism, in your case an E. coli. There is not much equipment involved when you do the transformation with competent E. coli cells. You would need vector DNA which can be purchased. Maybe a nearby microbiology department could donate some. The simplest experiment is to introduce a resistance to an antibiotic.
Antibiotics are compounds that kill bacteria, but bacteria can become resistant to it.
Another experiment you could do is to see which mutation is easier to introduce in E. coli, resistance to the antibiotic or tolerance for lactose. You would need to do some calculations to determine the frequency of mutation. Argonne National Laboratory, Division of Educational Programs, Harold Myron, Ph.D., Division Director.