Not an easy answer - depends on the type of limestone, the finish of the fireplace and its overall value / age. And the type of dirt you want to shift.
Some limestones are quite porous, so soot etc will work a mm or so into the stone, and the aim of cleaning is to get it out. This might be done by a solution, starting with detergent and water and seeing how it goes. Other limestones are almost marble-like, and these tend to be the pricey ones.
However - if the fireplace is an antique, the stone will have developed its own patina and this is part of the value. Vigorous cleaning will damage this patina, so take expert advice from a stonemason.