Where to start will depend on the appearance you are looking for. I'd start in the most visible location so that the parts you see most are the parts with the whole tiles rather than partial tiles. However, this probably means starting near the middle which will mean both sides will have partial tiles, requiring more cuts. Another option is to start in a corner so that a row of whole tiles runs along two sides of the hearth (I am assuming it is some sort of rectangle shape). This will mean the largest number of whole tiles and fewest cuts. When I put slate tile on my porch I tried to match the thickness of adjacent tiles as much as possible, but did not adjust the mortar thickness. The result is numerous joints that aren't quite even but it is not nearly as noticeable as I first thought it would be. Slate will crack if there is any gap below it so I don't think shims are a good idea. Use a nice even layer of mortar and live with the differences in tiles thickness is my advice.