First, if you desire a saddle (a flower holder that clamps to the top of the stone), you can obtain one from your local florist. Be sure to ask the florist for stainless steel, since plastic-coated clamps can crack, allowing the metal to rust and then permanently discolor the stone.
Second, if your stone is located in a place where mold is likely to grow, such as under trees or in areas where other stones show signs of mold, consider buying an all-polished stone. This will prevent mold attachment and growth.
Third, when purchasing an upright monument, consider the size of the base. Many monument companies only allow 6″ on each side of the upright stone, which does not allow much space to add a vase to the side of the stone. If a vase is ever desired in the future, it can make the monument less stable. The stone will be less likely to settle or sink with a wider and longer base.