A barrier of polyethylene, cement backer board, then the stone.
Man made stone varies all across the country. It has very high shipping cost so, it may be best to find something made near your home and pick the best looking from that. If the fireplace has stone on it now, you could take a picture of it and try to match it.
In my area there is a brick company that makes bricks 3/8" thick and can match several colors and styles of brick. That might be an option if your fireplace is brick, just remember the shipping cost.
Limestone rip-rap (stones measuring 3 1/2" to 6") is available almost anywhere in the world and, when laid artistically, it makes a nice looking wall. It may also be the most economical to use since you buy it by the ton on a dump truck.
Let us know how you come out and we love pictures.