Is there a rule which inversion ( a, b or c ) to use? 

 - when playing SingPlay style, as there is no melody, just accompaniment, you have the choice of any inversion (a, b or c) when playing ProPlay (ie with the melody ) then the melody has to be the highest note and the inversion you choose is one that has the melody not at the top. 

Eg for chord 1 if the melody note is note 5, then you play version a - if the melody note is 1 then you play b and if its note 3 then you play version c.