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If an airplane is flying north, from what direction would the wind be blowing to most effectively cause the aircraft to veer toward the east?

What sort of path would it follow for the first second or so? 

It would accelerate toward the east, progressively picking up speed in that direction, while continuing to move toward the north with little change in its northerly speed.  This would cause its path to curve toward the east.

If the wind keeps shifting so as to remain perpendicular to the direction of motion what path will the airplane follow?

If the wind remains perpendicular to the airplane, it exerts no force in the direction of motion so it neither speeds the airplane up nor slows it down.  The path will continue to curve to the right, and it will fly in a clockwise circle.