The project statement should be extremely readable since committees are working quickly and must be able to grasp a proposal on the first read.
The majority of Fulbright review panels are interdisciplinary. Imagine your reader is an intelligent non-specialist in your field and strive to make your proposal clear to that person.
An orienting first paragraph that outlines the what, where, when, and how of your proposal prepares your reader for what is to follow and helps you define the rest of your essay.
Avoid complicated sentence structures.
Avoid field-specific jargon and define those technical terms you must use.
Avoid the tendency to give a lot of background information. Fulbright is more focused on what you will do.
Don’t hesitate to recognize your own agency in the project. Feel free to use the first person rather than passive. Also be declarative rather than tentative – “I will study the effects of…” rather than “I will attempt to….”
Include your preparation for the project. Prior coursework or research experience, relevant foreign language ability, specific skills like excavation, GIS, paleography, etc. can all be important.
Choose the field of study category wisely, since the label you choose will condition the expectations of the reader. There is an "interdisciplinary" category as well as others that are broad enough to encompass a variety of topics.
If you do not speak the language of the host country, include in your proposal how you will learn it, even if it isn't necessary for the success of your project. Fulbright sees its grant recipients as ambassadors and seeks people who will engage with their host culture beyond the scope of their research.