Good Afternoon, Bitterwheat;
First and foremost, it takes a desire to join GAF; no uniforms are required. (Uniforms are nice, and desirable, but not required) What you have already is a good start; it's up to you to decide whether or not to acquire additional items of uniform to flesh out your impression. (Most of us in GAF do...)
You can find some basic information at
http://www.grandarmyofthefrontier.org, including organizational charts, military uniform specifications from the Victorian era, etc.
Being in Florida, you are in the "Department of the Atlantic", Colonel Bull Schmidt commanding. You might want to send him a PM introducing yourself (if he doesn't see your post first), and have a brief chat with him to discuss the GAF in general and any role you would like to play in particular.
I have the honor to remain,
Your Obedient Servant,
Bvt. Captain Malachi Thorne
Commander, US Marine Detachment
Department of the Pacific