Jim,
Chefboy has some good advice.
The main thing is to have respect for your employees so that they in turn can respect you.
Be consistent! Which with 15 things going on at any given moment that can be difficult. Be consistent, clear about expectations, but also document everything!
I spent a lot of time with my first union shop management position learning the system -- and prehaps one of my proudest moments was when I had had a grievence filed against me and another union employee went to bat for me with the union (because of respect, consistency).
Yes, you will hear "it's not my job." expect it, and now how to deal with it -- often union job descriptions have a phrase in there about "any reasonable task as set forth by management" As long as you are not consistency asking someone to work "above their grade level" you should be fine.
Show confidence and not intimidation and you'll be fine!