Natural swimming ponds do best when lined with durable, flexible, and non-toxic liners. A geomembrane matches all these requirements. Geomembranes are flexible, tear-resistant, and don't leach any chemicals within the material. Concrete and fiberglass are more difficult to install, and much more likely to crack or warp and require serious repairs.
Because you'll be using your water to encourage plantlife and for humans to swim in, its important that no dangerous chemicals are allowed into the water. Some liners degrade quickly after time or use, and will begin to leach toxins into the water.