The first act of The Merchant of Venice is full of drama, passion and intrigue. We are introduced to a melancholy Antonio, Portia--angered by her late Father's wishes--and Shylock with his infamous "pound of flesh."
The main focus of Act I.i. is Antonio and the cause of his distress. He claims that he is not concerned about his ships as "my ventures are not in one bottom trusted," nor is he in love. There has always been speculation that Antonio's feelings for Bassanio are more than friendship but there is no proof and this is all down to speculation. Antonio confirms that he will do anything in his power for his friend Bassanio in the pursuit of "fair" Portia.
Music that would set the scene here would be slow (to suit Antonio's mood), building up when there is talk of love. "PS; I Love You " by the Beatles speaks of love but is non-specific which would suit the setting. A more classical edge would be Beethoven who had some similar issues as Antonio--aware that something was missing in his life (hence Antonio's melancholy)--but never being quite sure what it was. Choose one of Beethoven's sonatas or symphonies. This will also add drama for the whole act.
In Scene ii, Portia must deal with her father's will and the three caskets. Portia, an independent woman, knows she cannot control the matter at hand but will try and steer her suitors so that she is left with the only person she is interested in, Bassanio.
The tunes from Les Miserables (the stage show) would also fit this act of The Merchant of Venice, especially due to its recent popularity with the introduction of the movie. The most famous song is "I Dreamed a Dream" is a soundtrack for the movie.
The Phantom of the Opera would be another possible choice for this act. Shylock in scene iii and the pound of flesh is reminiscent of the "final threshhold" and the "point of no return."