Popular music would have been commonly heard in the streets, taverns, festivals, at home, in plays, etc. It was more of an oral tradition, passed between musicians and handed down over generations, and little of it was written, so we don't know much about it now. Shakespeare makes many references to music, so it must have been well enough known to his audience that he felt they'd understand the references. Those living in bigger communities would have had many more opportunities it to hear music than smaller villages, especially since travelling musicians would have gravitated toward the larger towns and cities. Small villages would have been just for an overnight stay and and a meal, but a travelling musician would have been a real treat for a place like that.

Sacred music would have been heard in churches, and again, the size of the place would have made a difference. A small town might only know the major hymns, while a large church in a major city might have their own musical director who composed a lot of music.

Classical music was firmly in the Renaissance period in 1500, and in England the most prominent composers of the period, Byrd and Tallis, were yet to be born. By the end of the Rennaissance, approximately 1600, florid polyphony was the style. Before 1500 classical music in England was in it's infancy, with little classical music of note with one enormous exception - John Dunstable. Until this time, most harmony was based on octaves and fifths, but Dunstable developed the first harmonic vocabulary based on thirds and sixths, a harmonic tradition that was quickly adopted throughout the world and continues today. Little of his work survives, and after him, England didn't contribute much to secular composed music until Tallis and Byrd in the mid to late 1500s.

So 1500 was kind of a quiet period in English secular composed music, although such composition was very active in Germany, France, and Italy. In England, the opportunities to hear music other than popular street music and sacred church music would have been available, but probably confined primarily to the aristocratic classes. There would have been very little opportunity for the average person to hear "classical" music.

From what I have been taught, written/art music (what you're really referring to in the question) was more in the realm of the nobility and aristocracy. A famous example is the English "Chapel Royal", which historically catered to the nobility and featured people like Byrd, Tallis and Purcell (as a treble).

The main issue with folk music is that it was not tabulated regularly until proper notation occurred in the 17th-18th centuries, and so popular music from the time is impossible to hear sadly. We have copies of chant books from the 11th century (after the Gregorian reformation of chant) and so that is a little less emphemeral as far as harmony and structure are concerned.

There is loads of information about them, one source I found on Wikipedia was "The Early History of the Chapel Royal" by Hillebrand (I have only read about the Chapel Royal in encyclopedias, the names of which evade me). Another big source for me is the Norton History and Anthology of Western Music, which are great overviews of the history of music but use broad strokes.