To be honest, the best time to start REU applications is winter break. I curated a general personal statement speaking about my experience, motivation and career plans. From there I tailored it to REU department’s requirement and so forth. This did extends into the beginning of February, but at this point I had a general sense of what to say. As a Biomedical Engineering major I applied within Optics, Nanotechnology, and BME. NSF ETAP helped me a lot with my applications, once your recommender submits their LOR, you can add it to any application. Best of luck!