Have an Answer?
Believe it or not, this is an easy answer..and most likely an answer you've already provided for yourself. The type of engineer you "should" be is a direct result of your interests. For me, I looked at my hobbies (which included taking things apart) and was interested to see that I had no preference as to what I was taking apart, rather I liked the activity itself. Rather than being focused on the Electrical, Mechanical, Structural, or other areas of the object I was taking apart, I was focused on the overall activity. That led me to be a Construction Engineer, which puts me in a job-role to be a part of the "overall" of the project I am on, rather than any individual detail.
Answer for yourself: Do you like Elecricity (Electrical Engineer)? Do you like moving parts (Mechanical Engineer)? Do you like working with dirt (Civil Engineer)? Or does the opportunity to work on a broader level (like, I want to build a building) attract you (Construction Engineer, Construction Managment)? The answer is probably very obvious to you.