how long did it take for classical instruments to work there way down to the lower classes?

Today, classical music is radically different from the music most people are familiar with. In the past, it was not that extreme.

Yes, a lot of what we call classical music developed among the upper classes. But its language, so to speak, was much closer to the language of the music most people were into. The instruments were also closer than today. Of course, you could find expensive versions in the rich courts and cheaper ones in the hands of struggling musicians, but there was some overlap in the type of instruments both sides were using

Many guitar-like instruments were used in the past, for all kinds of music. The guitar was not exactly an exclusive product for/of the classical tradition, it's a modification of those earlier instruments. The same for the violin, there were fiddlers playing other kinds of music.

The piano is kind of an exception. It started as a rare thing, and at first you could only find it in the rich courts. Then it made its way "down." It was not until the second half of the 19th century that you see mass produced pianos. Cheaper designs were made to produce cheaper pianos (squared, upright, and then spinets), the grand piano has continued to be an expensive instrument.

It should also be noted that stringed instruments were not exclusive to Europe, and African cultures have their own stringed instruments, such as the Ngoni (Konting), Kora, and Bolon. Slaves brought to America would have been familiar with these stringed instruments, and it is known that slaves were able to recreate their instruments once across the Atlantic, from which we get the modern banjo. This tradition would have been carried down to sharecroppers. Adopting the guitar into their musical culture would not have been terribly difficult, as it would've been seen as a variation of the plucked string instruments they already had knowledge of.

Sources: http://www.digitalhistory.uh.edu/era.cfm?eraID=6&smtID=6 http://nationalhumanitiescenter.org/tserve/freedom/1609-1865/essays/africa.htm