Child Safety Fireplace

I have purchased a home with a wood burning stove in the living room. It sits in a corner. The corner is brick on the floor under the stove and all the way up to the ceiling. The insurance company is coming to inspect the stove this week for safety, but it is new and I am not too concerned about the safety the way it is now. It is fairly clean and looks new. The previous owner put trim up at the top next to the ceiling, but did not paint it. Is it safe to paint? If so, is their a certain type that is best to use? We had a stove in our family room when I was a child, but it vented into the fireplace, so I have no experience with this situation. What advice can you give me about using the stove? If you are going to say something stupid like sell the house, go answer another question.