The International Society of Arboriculture promotes the professional practice of arboriculture and fosters a greater worldwide awareness of the benefits of trees.
wwv.isa-arbor.com
Depends on what you are doing and what you want to do.
To me Certified Arborist is a bit of a "no brainer" for anybody who is going to do this as a career. It is not that expensive. Continuing education is easy to come by...I'd be going to learning opportunities anyhow to learn regardless of counting hours. You can certainly be a great arborist, and never be a Certified Arborist. But it at least shows some level of commitment to the profession to somebody looking in from the outside.
From there...what else are you doing?
Climber specialist, Utility specialist, or Aerial lift specialist is probably good if you want to have some "employment flexibility". If I am hiring you and you have one or both of those, it lets me know you have at least some base of correct knowledge and that you have some level of commitment to the job. If you are happy where you are and never want to move...or are an owner, those probably don't matter as much because they don't mean anything to a customer.
Probably about the same with Municipal specialist...except I think that holds a little different value to clients if you are doing municipal consulting. That is something municipalities should recognize a little more.
TRAQ
https://www.isa-arbor.com/Credentials/ISA-Tree-Risk-Assessment-Qualification (don't need to be a Certified Arborist first). If you are advising others in any official capacity, probably a good qualification to have. Provides them a level of confidence.
BCMA. Frankly, I'd probably not have done that except a few years ago I was invited to take the test for half cost (and a free retake if necessary) as they were looking for "beta testers" when the made some changes. I debated with myself for a while and decided it would feel like a good personal achievement. I'm glad I did do that, it felt good when it was done. But the reality is that feeling plus $4 will get me a cup of coffee most places, right? Most clients around here don't recognize that as a different qualification. I have been told though that in more competitive markets (Columbus, OH I was told) many clients are beyond asking for a Certified Arborist - they are now asking for a BCMA. that is not the case here. Again, BCMA is probably good if you are looking at other employment opportunities.
My $0.02. take it or leave it. Others will disagree, and I am OK with that! Their opinions are based on their observations and experiences so they have just as much validity as mine.