When asked to weigh in on the question that’s so popular, some thoughts that immediately come to mind are:
a) If possible, begin with management consulting. It is more difficult to find a product management job that allows one to do management consulting-like work than it is to find a management consulting job that will enable one to do product management-like work.
b) If you begin consulting, communicate with your resource manager or director to work on product management projects.
c) Companies that provide innovation consulting may be worth investigating; however, this will likely depend on what aspect of product management you enjoy the most (e.g., management versus creation)
PARTING THOUGHTS
As a final thought, combining the two disciplines is probably not the easiest thing to do. Other options include working for the professional services side of a product company, as part of an incubator, or as part of a turnaround firm, but these would not be among my first recommendations.