You've got little time and a huge amount of work ahead of you. I also think you should go with an ARF trainer. I'm going to go against my usual advice and suggest that you consider an electric ARF. I say this because you can get a nice park flier, radio, and basic equipment and stay within your budget. The really cool part is if you get some help learning to fly, and put in enough time with the plane and simulator, it's quite likely that you can not only show the plane to your teacher, you can take it out to one of the school fields and do some demo flights. Doing the paper should be easy. Take some pictures as you're assembling the plane. Read up on how a proportional radio system works and then provide a summary. Explain each of the control surfaces and how they effect the flight path of the plane. Throw in some stuff on how the wing generates lift. Should be more than enough to ace the project.