I would say that you should just concentrate on getting that license first. Once that valuable piece of paper (book) is in your hand, you should just pound the pavement with everyone else and take any job that you can. Experience is what you need and likely have little of at this point. Keep in mind that you are entering a field which has a lot of experienced engineers that are also job searching.
To go union or not is entirely up to you. I sailed many years in MEBA and hold them in high regard. AMO on the other hand, not so much. There are pluses and minuses to either one. A big plus is the paid training at a world class facility (Calhoon MEBA), defined benefit pension, medical, dental, etc. The downside is that there are far less deep sea jobs available now and a lot of people waiting in halls for those jobs. Non-union companies can be very good, sometimes better than a union, and sometimes downright third world-like with little pay and crappy benefits.
Just get out there and get some type of experience, eyes and ears open, continue to learn, work towards upgrading your credentials, and then you’ll be able to be a bit more choosy.