If the brick has no heavy soil or deposits, or any white powdery deposits, you can prepare by brush vacuuming, and wiping down. We can discuss other cleaning methods if needed. Is the brick porous or slick? For our primer on tight (non-dusty) brick we like a pigmented Elastomeric Primer. These primers are designed to tolerate high alkalinity of concrete and mortar, tie up slightly dusty surfaces, and provide a great foundation for 1 or 2 coats of 100% Acrylic Interior Paint. If the brick is slick or shiny, consider Coronado 116-11, Benjamin Moore #066, or similar product. The primer is most important product of your system. The primer is thin for penetration, so don't try to get full hide-just seal the brick with a uniform coat. You will roll on primer, then use your brush to work into any deep mortar joints or cracks, then rolling over again. Watch for puddling and runs if mortar is deep or inset. I would use a 6" mini roller, sometimes called a "Long John" or "Popcorn" roller, and a 2 1/2 inch angled brush. The roller will allow you a controlled application. Work a row or two at a time, starting at the top and working down. Take care not to get a lot of material on the next row, because if it dries a little and you reapply over top, it will cause lap marks. You should use this similar method to apply your finish coats.
Where the brick meets the wall and ceiling, you could use our Painters Tape - (PURPLE for surfaces painted with flat paint especially ceiling) and our GREEN for all other surfaces, so you could roll right to the edge of the brick. It is difficult to "cut in" with a brush on brick as the surface is rough, especially mortar joints. If edge of brick is trimmed in wood, just tape with GREEN Painters Tape.
Once you get the brick primed, you want to decide if caulking is needed to fill cracks or holes for a smoother look. If some of the mortar is damaged, we like VIP's Kover Krack Textured Elastomeric caulk. It has a grit in it to simulate the look of mortar. You can tool it to match the appearance of existing mortar. Use smooth grade if just filling small cracks or pinholes.
As far as the finish paint, you can use any top grade 100% acrylic finish. Flat is O.K. but if brick is rough, it may tend to gather dust over time, so you may want a little sheen for easy dusting. You can even step up to a semi-gloss for your final coat if you prefer that look. Bottom line, any top grade acrylic (2 coats after priming and caulking). Sheen of your personal preference. Paint only the exterior surfaces. This is not for brick or stone inside the fireplace opening.
We like Coronado's low-sheen flat Tough Walls (prod# 24-1), or Velvet Acrylic (prod # 34-1). Benjamin Moore Regal Velvet also is a good choice. All products are waterbase. For the hearth, use a Semi gloss finish. For simplicity, you can certainly paint brick, hearth and mantel all semi-gloss or gloss if you want it to stand out.