Here is an easy melody to play on guitar. "In the Hall of The Mountain King" composed by Edvard Grieg in 1875. It is a song that is instantly recognizable. I teach this song to many of my students who are in the first stages of playing the guitar.
Below is a PDF of the Guitar Tab that you can print out as well as an audio file of the melody.
PDF - "In the Hall of The Mountain King" Guitar TAB