If the wood-burner is in use, and these bricks get hot, you will need some sort of high-heat paint. I would suggest stopping by your local Sherwin Williams store. Since they are a company with a complete line of coatings, including industrial ones, they are likely to have one that can help you, or they can order one for you.
If the bricks do not get hot, you should use a primer intended for masonry, and then any high-quality wall paint. If the bricks have any kind of soot on them, you will need to prime with a shellac-based primer, such as Zinsser BIN. (Use a respirator if you go that route... it is nasty stuff.)