Books on architecture in his high school library influenced Teague's desire to become an artist. At 19 years old, Teague left Indiana for New York City. He studied painting from 1903 to 1907 at the Art Students League of New York, where he met his first wife, Celia Fehon, a fellow artist. To earn money upon his arrival in New York, Teague checked hats at the Young Men's Christian Association in Manhattan, where he also began sign painting. His lettering work evolved into illustration projects for mail order catalogues, for which he drew apparel items such as neckties and shoes. Refusing involvement in the fashion industry, Teague focused his creative efforts on elaborate advertising illustrations, which caught the attention of Walter Whitehead, an advertising executive whom Teague had met at the YMCA.