“If you don’t know where you are going, you will probably end up somewhere else.”
Laurence J. Peter. 2011, The Peter Principle: Why Things Always Go Wrong (p. 145)
The Traditionally Perceived Project Manager Career Path
There is a perception in our profession that the following graphic represents the traditional career path for project managers. Either one starts on a project and moves forward, or is thrown in to take on the role of project manager. Either way, from then the project manager can grow to become a major project manager, or projects manager and then evolve to become a programme manager and then a portfolio manager.

My Concerns with the Traditionally Perceived Project Manager Career Path
Though I do not have specific statistics or studies to formally back this up, my 30+ years in the business working with leading international project management associations, trainers and standards development… and having had the unusual experience of actually having held all of these positions… I can say with a fair amount of certainty that it is a very small percentage of our profession that would have the opportunity, personality, training, or even access or desire to take on all of these roles.
Recommendations for Considering a Career Path in Project Management
Let us start with a general assumption around the basic competencies of project management. The International Project Management Association (IPMA) recently released the IPMA Competence Baseline 4 edition (ICB4), which is a brilliant reference that provides the key competencies for project managers (and one could argue project team members), as outlined before:

So, suppose that you are just starting out in the project management arena. Maybe you have a junior designation, diploma or even a project management degree or masters degree. What should you focus on? Do you have all of these disciplines and social / emotional / cultural intelligence skills and capabilities?
The simple reality is that the project management / change deliver industry and clients have invested bazillions in training, courses, certificates, diplomas, degrees, masters, PhDs etc. that may or may not have benefited the success stats of projects worldwide. Many taking these courses often do not have the experience, background, emotional / social / cultural intelligence, personality, capacity or competence to be project managers at that time. That should not stop them from entering our industry though, as there are numerous options available that could lead to a career in project management or other positions.
First though, I would suggest going back to basics. Take a look at the following:

This image shows the basics that project team members should have a general understanding of.
(This next section is a duplicate from the blog post The Evolution of the Project Management Profession, and the section called Modern Project Management Competencies and Discipline.)
The basics include a solid understanding of the following:

A simpler model is below…

If you are not solid in these areas you have no business pursuing work in this game.
If you start with the basics, such as risk management and project controls, maybe you will find out that your passion is risk management, cost engineering, schedule engineering, values management, benefits management, business analysis and business cases… or maybe you will lean more towards project management as outlined below.

If you want to get ahead of the game though, get proficient in the organizational focus of sustainability and social responsibility… which adds another layer of complexity and interest in the project management space, and makes you far more valuable to the organization.
If we combine these, as we did for the GPM360° Registered Assessor and Consulting (RCA) program where we focus on raising awareness and competency around sustainable project management with the following skills (as well as the assessor and consulting skills), we get the following model skills:
No matter what career path you choose, having an awareness of a number of skills, including sustainability, can provide more value to your clients and will help to differentiate yourself.
REFERENCES:
Carboni, J., Gonzalez, M., & Hodgkinson, J. (2013) The GPM reference guide to sustainability in Project Management. Fort Wayne: GPM Global. http://www.greenprojectmanagement.org/the-gpm-reference-guide-to-sustainability-in-project-management
GPM. (2016). The GPM P5™ Standard for Sustainability In Project Management v1.5. Novi: Green Project Management.
GPM. (2012). PRISM PRojects Integrating Sustainable Methods. Green Project Management.
Humphreys, G. C. (2014). Project Management Using Earned Value, Third Edition. Retrieved September 21, 2015, from http://www.humphreys-assoc.com/evms/project-management-using-earned-value-third-edition-p-71-c-11.html
Humphreys, K. (1991). Jelen’s Cost and Optimization Engineering, Third Edition. Retrieved September 21, 2015, from http://www.amazon.com/Optimization-Engineering-Humphreys-Kenneth-Hardcover/dp/B010WFHHB2/ref=sr_1_9?s=books&ie=UTF8&qid=1442859945&sr=1-9&keywords=jelen%27s+cost+and+optimization+engineering
IPMA. (2015). IPMA Competence Baseline (ICB), Version 4.0. International Project Management Association. Retrieved from http://products.ipma.world/ipma-product/icb/