In the first chapter of his autobiography, Poetry and Truth (Dichtung und Wahrheit), Goethe describes the effect on him of the puppet theater presented to him and his siblings by his grandmother in 1753. (His little brother Hermann died in 1759.) This account is followed by Goethe's first biographer, the Englishman George Henry Lewes (1855), who wrote: "The dear old lady, proud as a grandmother, 'spoiled' them of course, and gave them many an eatable, which they would get only in her room. But of all her gifts nothing was comparable to the puppet-show with which she surprised them of Christmas eve of 1753, and which Goethe says 'created a new world in the house.' The reader of Wilhelm Meister will remember with what solemn importance the significance of such a puppet-show is treated, and may guess how it would exercise the boy's imagination."
According to Metzler's Goethe-Lexikon, the puppet theater was an important source of "moral-didactic" entertainment from the 17th to the 20th century. In Goethe's time favorite themes were Old Testament stories and fairy tales. He probably also became familiar with such traditional German folk figures as Hanswurst, a frequently obscene stock character of comedies and other plays, and Doctor Faustus. His most famous play is based on the Faust legend, but in 1775 Goethe also wrote a drama fragment entitled Hanswursts Hochzeit oder der Lauf der Welt, which contains over 200 scatological terms and insults describing the wedding guests.
According to Nicholas Boyle's biography of Goethe, it was actually his father who gave the children the puppet theater. I think Boyle is correct in salvaging the reputation of Caspar Goethe, who could hardly have been the pedant he has been portrayed to be.
The charming picture above (click on image to enlarge), showing the boy Goethe peering from behind the stage curtain and judging the effect of his own puppet productions, is the work of Woldemar Friedrich (1846-1901), who illustrated many episodes from Goethe's life.