Use ordinary paint - you just need to take special care because the fireplace is a central feature in the room and your eye will be drawn to any mistakes.
If it is waxed, you need to clean the wax off carefully with white spirit before you start. (Paint won't stick to wax) then apply a thin coat of primer. Don't worry that primer looks awful - think of it as glue rather than paint. If it is varnished wood, rub it down with fine sandpaper before painting - and you won't need primer unless there are any places where the varnish has come off. Always prime bare wood.
If you're fairly new to painting, use a water based non-drip paint. Two thin coats will give a better result that one thick coat - whatever it says on the tin.
For best results, use old-fashioned oil-based undercoat and gloss finish. That involves putting the right amount of paint on - with the grain of the wood, brushing out across the grain, then finishing by brushing lightly with the grain using only the tip of the brush. To understand oil based paint, think of it as an oil coating that you have to stretch over the wood.
Just remember that the worst that can happen is you have to let it dry, sand it down and do it again :-(
