ACtually, I do allot of fireplace or brick painting where the situation like yours occurs. The job does not require alot of material expense, just alot of labor. Its more labor intensive than material expense.
First, I would clean the brick very well with vinegar and water. You want to clean off all the grime, ash, smoke stains, and whatever buildup there is.
Second, I would get some paintable caulk and fill in any cracks, holes, or blems. "paintable" is the key.
Third, get a gallon or two of Zinzer BIN primer and apply two or three coats of primer. Let each coat dry thoroghly between coats. You want a build up to hide the pores and get a semi smooth surface.
Fourth, painted brick looks best with a sheen. Semi gloss is fine but nothing under that. "in my opinion". The higher the sheen, the easier to clean the brick.
Fifth, apply minimum of two coats of finish paint. I use latex paint.
***get a 2 1/2 inch sash brush preferably a Purdy or Baker brand. They load up with more paint. You will ruin the brush painting brick as it sands down the fine hairs.
If you want some pictures of finish products let me know and I will email them to you.