Madame President the Vice President here.
With a post about The month of Miyazaki
Anyway back in March of 2006, Toonami got the rights for 4 movies and aired them one weekend after the other. These movies were Spirited Away, Princess Mononoke, Laputa: Castle in the Sky, and Nausicaä of the Valley of the Wind.
This was my First introduction to his work and the first four I saw.
Spirited Away is the story of a girl who ends up in a village for spirits and must find a way home. Released on July 20, 2001
Princess Monooke is the story of a villager cursed by a infected boar who travels to not infect his village and find out why it happened.
Released on July 12, 1997
Laputa is the story of a girl falling from the sky and the boy who finds her and tries to get her home.
Released on August 2, 1986
Nausicaä is the story of a girl who lives in a world ravaged by war in a village that tries to keep the infection of the forest from overtaking the village.
Released on March 11, 1984
If you notice a pattern the movie started out with the a newer work and went back to his earlier works.If you have people who aren't huge fans of anime, Spirited Away is a better bet to try and get them interested. The older works are good but some people will have issues with the art style.