Actually, he was 35.
Classical music was the first music I heard that I wanted to play, thanks to my mother who listened to a classical radio station, as well as an easy listening station, but since my parents were folk dancers that was also in the mix from the beginning. I got into jazz when I was a teenager, while listening to rock and soul on the New York AM stations. Country music came along after college, and there are a few disco classics in my collection too. However, I draw the line at rap, house, EDM, and hip hop. So even the most eclectic listeners may have their limits.
If I had to choose music to make the case for Mozart as one of the greatest classical composers I would probably choose some slow movements from his concertos: the clarinet concerto, the piano concerto No. 21 (if you can forget about Elvira Madigan), the Sinfonia Concertante; arias from "The Marriage of Figaro" and the ending of the opera, which can bring me to tears, the last scene of "Don Giovanni" when Don Giovanni entertains the ghost of the Commendatore, and the trial by fire of the lovers in "The Magic Flute" (I know opera is a hard sell but the music is worth the extra work); and some of the serenades: for 13 wind instruments, the Serenata Notturna, and the Haffner Serenade.
But everyone reacts to music differently and your mileage will vary. One of my classical music-loving friends can't stand Debussy, another has no use for Rossini, another who doesn't like Mahler, and so on, and so on.