What can I expect when applying for a logistics management specialist position?

Your question is near impossible to answer. 0346 series is very broad and encompasses everything with supply, transportation, and maintenance. That being said, usually one does not do all three at the same time. Usually they tend to be focused on one of the three areas. I held two different positions as a 0346. In one, I was focused on transportation, the other was supply. So there really isn't a catch all answer. Like Army units, each office is as widely varied as the next. The fact that the field is broad, will open some doors. I had a greater interest in project management and USACE specifically so that is why I left being a 0346. The experiences I gained were easily translated to project management so it worked out well for me.

All that being said, it can be a great field. You may want to look into the DA Intern program for logistics (http://www.cascom.army.mil/s_staff/clcmo/da_intern.htm). I think they still hire a couple of times a year. The program is pretty involved but is a lot of good training and OJT experiences. If you have an interest I can give you a POC who can fill you in more as I am a few years removed from that program. If you can get in to that program, it is a great path to start a federal career.