Violin motif
Philip's violin is more than just a tool by which he earns a living. It symbolizes his path to independence, since he earns money by playing it; however it is also an emotional connection to his father. When he plays it, sometimes he loses himself in the music. Playing is, for Philip, a personal and emotional experience. His audience senses this, and that (plus his surprisingly good technique) is what they respond to. A couple young women are particularly attracted to Philip's musicianship.
Twice, people in authority propose that Philip be forced to sell his violin to pay off a debt. Initially, Squire Pope wants the violin to be included in the liquidation of Philip's father's estate. Later, when Philip is the victim of Lorenzo Riccabocca who absconds with the proceeds of the evening's concert leaving only debts behind, a debtor proposes to force Philip to sell the violin. Cooler heads prevail in both cases, however the threat to Philip's livelihood increases the plot tension.
Doctor Goldsmith allegory
The famous author of "The Vicar of Wakefield" enjoyed a real-life series of travels as an itinerant musician, playing his way through Europe. Philip, having read his biography, mentally compares his travels and situation to Goldsmith's.
Money as symbol of adulthood
Throughout the novel, Philip is unwilling to have other people pay his way. Instead of acting like a dependent child, Philip insists on paying ten cents for his room and board at the Tucker residence. He pays his debts, and the costs of the concert, after the Riccabocca disaster. He refuses to allow Squire Pope to manage his money (which, as his guardian, Squire Pope would have been within his rights to do). When he meets Henry Taylor, a boy about his own age, Philip steps into a quasi-parental role. It is he who pays their traveling expenses, who gives Winuca a gift after having accepted his lodging and board, and who controls his money. He refuses to let Henry care for any part of it.
One of the things that defines Philip as an adult (as opposed to a child) is his ability to earn his own money in exchange for valuable services to others.
Clothing as symbol of class change
In the final chapter of the novel, Alexander Taylor rewards Philip for the safe return of his teenaged son Henry. Part of the reward is a trip to the tailor for some new clothing so that Philip can join Henry at an upper-class boarding school in Connecticut. A new suit of better quality clothing is a frequent way in which Alger signals an impending change in socioeconomic class or fortune.
Buggy or carriage as symbol of prosperity
The means of transportation the characters use in The Young Musician is significant. People without money walk about on their own two feet, as Philip Gray and Lorenzo Riccabocca do prior to earning significant money at a concert. People of moderate means or who are occasionally wealthy travel by train if they have to go a long distance. Some of the farmers have horse-drawn wagons which they use for work. But the people who are really successful own horses and carriages solely to travel about. A buggy, which is a small carriage, cannot be used to transport animal food or significant portions of trade goods, so the only people who own or use them are those who are wealthy enough to keep animals and equipment solely for locomotion. The innkeeper, Mr. Gates, possesses a buggy. One of the ways Mr. Gates shows his faith in Philip and his support for the young musician is by offering to drive him to the next town so as to track down the nefarious Riccabocca.