What kind of show Quiet Please is

 To define the entire series is elusive. Often times labeled as "Horror", but that's a bit deceptive, though that is the genre in which some of these episodes fall; For example, the episode entitled "The Thing on the Fourble Board" is consistently awarded the unofficial honor as being: "Best radio horror show of all time", and more so, best radio drama ever.. which all may be very well true, but that's only one of the episodes, there are 104 more, some having nothing to do with monsters, or other things that go bump in the night. 
Other episodes - though still surreal - focus towards spiritual obligations, effects of actions, and personal responsibility, or simply a look at life from a different perspective...
The point is, as a whole, it's really not a horror series.
Perhaps the most accurate classification would be "Fantasy".
How ever you decide to define it, one thing can be agreed upon; the series was very original, and the first of it's kind, with it's signature laid back atmosphere.

Episode #59 August 9, 1948.
The Thing on the Fourble Board
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Two workers on an oil rig discover something strange brought up from a mile underground, and then something comes to get it back...
This is the most famous episode of the Quiet Please series, and holds claim as the best radio drama of all time. Audio quality is great.