Mary Moysey looked and looked this past winter for the best school to which she could send her two sons in the fall.She and her husband finally settled on Great Falls Elementary School in Fairfax County.

The Moyseys, who live in Montgomery County, then proceeded to buy a house in the neighborhood served by the Great Falls school. On Feb. 14, they signed a contract to purchase the $100,000 house and gave the realtor a check for $5,000.

Four days later, they got the bad news - their neighborhood would not be served by the Great Falls Elementary School next fall. Her sons would have to attend an elementary school in McLean.

"I was furious," Mrs. Moysey said yesterday "The school was the exact reason we brought the house. We tried to back out, but we will lose the $5,000 if we do."

So the Moyseys have decided to buy the house.

Because of overcrowding at the Great Falls Elementary school, a school spokesman said some parents in the area have been notified that their children will have to go to Spring Hill Elementary School in McLean.

Great Falls Elementary School, at 701 Walker Rd., is the only school for kindergarteners through sixth graders in the area. It has an enrollment of 857 students, 134 more than the school's capacity, a school official said.

Mrs. Moysey said she was impressed by the Great Falls school because of its emphasis on basic instruction in enclosed rooms for individual classes.

School spokesman George F. Hamel said a new elementary school is scheduled to be built in the Great Falls area next year. However, that school, which was approved in Tuesday's bond referendum, will not be ready for use until 1980.