I disagree with you "Grumpy"
EMS is the most underpaid and unrecognized allied health field. Firefighters, police officers, nurses, respiratory therapists, and etc all are represented by unions that have organized the profession and gotten not only increased benefits, better pay, and retirement, but also respect for their members.
Some areas, particularly rural ones where there is not always an organized professional system to follow, may find union representation extremely valuable. When some organizations are side by side with volunteer services the pay scale may be completely unsatisfactory for a professional.
I cannot give you much advice, however it is important to consider exactly what the union you are considering offers. At what capacity is the union going to be able to represent it's members? If certain members elsewhere strike are you required to strike as well, even if you are not connected or even do not support their reason for striking? Besides monetary dues, what else is required of membership? Can management be members of the union? If you are not in control of benefits/payroll is the person(s) in charge going to be able to meet demands? Is your administration going to be able to meet and maintain the demands of the union? Do they necessarily have to? Is your building, policy, operations, and bylaws of your organization supportive of having a union representation? Do local laws conflict with union representation? What is the contractual agreement for membership and how long is it? How do you terminate the contact, or can you if you are unhappy with the representation? Are all (or majority) of the members of your organization interested in joining the union? Do all members of the organization have to be part of the union? And most importantly... what is your reason for wanting to be represented by the union?...is it a reasonable expectation?
Of course these are questions for you to ask yourself or the union representative themselves.
I am sure there is much more to ask and I may or may not have hit on some key questions. The point is, be well informed and well involved in something as important as this.