Drum sets were first developed due to financial and space considerations in theaters where drummers were encouraged to cover as many percussion parts as possible, says Wikipedia. Up until then, drums and cymbals were played separately in military and orchestral music settings. Initially, drummers played the bass and snare drums by hand, then in the 1890s they started experimenting with footpedals to play the bass drum. William F. Ludwig made the bass drum pedal system workable in 1909, paving the way for the modern drum kit.
By World War I drum kits were characterized by very large marching bass drums and many percussion items suspended on and around it, and they became a central part of jazz music. Hi-hat stands appeared around 1926.