It's all about exploring the more unpredictable aspects in the character, not just fighting people.
If you watch the show and the characters don't look at each other while they're talking, the actors probably aren't getting along.
I approach my character with the question: What would an animal think? How would an animal respond? A lot of times, it's quick action and no fear, and sometimes it's irrational fear. You don't always know.
I read every script from beginning to end, and I read every draft that I can. I like the show, I like the character, and I want to protect both of those things.
The most important thing is to just be good at what you do. You do a good job playing the character, and people will be taken up with your character, not your clothes.