Speak with the community or publis affairs department. Most will provide 'free' advertisements in their community bulletins and announcements. While money should not be the reason essays are written, it is an excellent enticement for those facing the expenses of future education. Both the State and Post level contests should consider a monetary award. This type of award should be in cash.
Savings bonds are attractive, but mature after the student is finished with school.
A small trophy or plaque is also good as they will display it in a conspicuous place, and provide more exposure to the students family, friends and classmates. Share this information with your ladies auxiliary. They may wish to contribute a small gift to the student. Keep in touch with your educators. Let them know that this is a worthwhile contest, and that you care about it.