In terms of study, what path should one take to become a project manager?
First, unless you have several years of project management work experience, I would suggest obtaining the Project Management Institute's (PMI's) Certified Associate Project Manager (CAPM) certification. After that, study the qualifications for the Project Management Professional (PMP) certification and create a plan based on those qualifications. The plan should include studying PMI's Project Management Body of Knowledge (PMBOK) Guide and added studies based on the PMBOK Guide's process knowledge areas.
Second, familiarize yourself with the International Counsel on Systems Engineering (INCOSE) Systems Engineering Body of Knowledge (SEBOK). After achieving PMP certification, pursue INCOSE's certifications. PMI certification will give you a top-down perspective across all departments whereas INCOSE's certifications will give you a bottom-up understanding of the engineering processes and products.
Studying these two knowledge areas in this order should provide a faster path, on paper, to project management and beyond. However, if you would prefer a career path leading to a Chief Engineer title, you might reverse the order. Pursing Engineering in Training (EIT) and then Professional Engineer (PE) certifications would be valuable on the technical career path, too.
Third, study people, develop lots of relationships (focus on the personal aspects and what you can do for them, not on what you can get out of them), and find at least one mentor other than your supervisor. These are critical.