There's really no best answer for the management style question. The point of the question is to see if you fit into their culture. You might want to sum it up in four or five sentences. "Coach" may or may not be enough for your interiewer because then you may be asked if you're Bobby Knight or Phil Jackson.
Your best attributes are, well, what you think are your best attributes.
You have to turn your worst attributes into positive ones. Getting too involved may or may not be "bad" depending on the company you're working for. A good idea is to concentrate on a bad aspect of a trait, but make sure you emphasize the good part. For example, you could say something like
"my coworkers always used to tell me that I was too involved, but I couldn't help it. I love every aspect of the kitchen, and sometimes this involvement helps me understand the workings of various departments. I would never have learned how to make a genoise cake if I didn't get involved in the pastry department."
Or something like that. Don't lie. Everyone can answer this question properly if you think hard enough. Do your thinking at home.
Josh, you should have a coupla stories where you turned a negative into a positive. Make it concise, don't make it an epic. For example, everyone has had the conversation with the boss about food cost. Sometimes we're asked to find a way to lower food cost. Did you succeed, and did you manage to find a way to better manage food cost?
Kuan