A very interesting question this, without narrowing the field down too much. Having played in bands that play Irish, American, Scottish.English and Cajun, I've heard and played a lot of tunes. I've had a little think, and I reckon that, of the many thousand possibilities, the tune that really lets an audience know they're hearing fiddle music is the Irish tune Cooley's Reel. However, playing this will not be a trick available to a beginner in the first week or two. For really top class VERY easy tunes, I'd say have a crack at Cripple Creek(USA) or Winster Gallop(England).