The main obstacles are work experience, knowledge and the feeling of management consulting. If you can, I suggest you take an MBA. Because your work experience is not enough, it is better to study while working in a management company, so studying is more suitable for an on-the-job job.
Consulting companies have advantages and disadvantages. The advantage is that you can do some new projects at any time, contact different customers, learn a lot of different knowledge, and help yourself systematize your understanding of enterprise management; The disadvantage is to do projects year after year, finish one project after another, and sometimes worry that there is no project.
So which answer to choose is up to you. As an HR worker, you should know that besides standing in line, not making mistakes, following the right leader, it is more important to set your own goals. Only when the goal is clear, your career choice is clear. I think this is your fundamental problem.
But don't worry, you are still young, and there is still a long way ahead. No matter what direction you choose, you will achieve something as long as you persist and don't give up easily.