do all the necessary cleaning and dusting
caulk all cracks, holes, dents, and defects
Prime with latex Zinser primer three coats at least.
when prime job looks good enough
Begin your finish coat. Use a latex Premium quality paint.
I always recommend latex because it dries so fast you can get on three coats in one day easily.
New unpainted fireplaces do soak up the paint, especially the mortar lines. I like a good heavy paint job on mine that I do.
Turns out nice, but remember, you will never be able to go back, so make sure this is what you want.