Which field of engineering gives me the greatest opportunities for advancement and flexibility to evolve/grow?
I personally would not focus on that. You should really do a deeper dive into each of those specialties, or jobs, and see what you would like best. Growth will come with expertise, but if you don't like your job it's all for naught. Any engineering career will provide awesome opportunities. Also look into petroleum engineering.
I am so excited to hear that you are looking at Engineering as a potential field. I can tell you I graduated with a BSEE and a minor in Business and for 30 years I have never been: 1. unemployed 2. I have had the flexibilty to work at home and be there as a mom for my kids 3. I have been able to learn and understand any technical issues that come up in my field. 4. I never get bored there are so many opportunities in STEM now. An Engineering background will only benefit you in the future whatever specialty you choose.
Veronica recommends the following next steps: