Douglas Adams knew from the start that he wanted to do something very different with the sound of the show. He wanted to apply the kind of production techniques used on, say, a Pink Floyd album to a radio show.
The Radiophonic effects, by Paddy Kingsland, Dick Mills and Harry Parker were groundbreaking. Few were purely synthesized, instead being made of a whole mish mash of whatever was lying around the studio. There's even a bit of Goons' batter-pudding-splat in one episode.
This also meant that recording the show was a unique experience for the cast. They often found themselves shut in small cupboards to record their parts, as the studio wasn't properly set up to record in multi-track stereo. Sometimes actors would be forgotten for hours, until small voices came over the microphones into the control booth, begging to be let out.
Douglas also knew from the start that he wanted a theme tune which was electronic, but that also had a banjo in it. Eventually, they settled on the Eagles' Journey of the Sorceror, but no-one can quite remember why the banjo was so important.