Start with the Air Force. Talk to OIC (officer in charge of the local recruiting station) and ask some general questions including what rank could I expect base upon my degrees and years with the church? Say s/he says 0-4. Then go the Navy reserve, ask the same questions. If the say 0-5, go back back to the Air Force and causally mention that the Navy is offering 0-5.... you get the idea. Before long, they will be following over themselves as Chaplin's are highly coveted.
Some other things you need to consider. You'll have to deal with folks of all faiths. Wiccan is a valid faith in the military as well a Buddhists and all the others. Don't think that you will be limited to whatever you are.