When should I start turning in this circling approach?
The FAA instrument flying handbook discusses techniques and the procedures by which circling approaches must be conducted.1

You must remain within the protected area or circling radii, but as soon as you enter this area, you may begin the circling maneuver.  Usually, this means you will begin the maneuver well before the missed approach point.  In particular: 

a) "The criteria for determining the pattern to be flown are based on personal flying capabilities and knowledge of the performance characteristics of the aircraft. In each instance, the pilot must consider all factors: airport design, ceiling and visibility, wind direction and velocity, final approach course alignment, distance from the final approach fix to the runway, and ATC instructions."
b) "Fly no lower than the circling minimums until positioned to make a final descent for a landing." (page 10-20 of Ref 1).