Just like the wetsuits for scuba diving, freediving and spearfishing suits come in either one or two-piece design. Both freedivers and spearfishermen usually prefer two-piece suits, because they provide more mobility and some additional warmth at the core. Many spearfishing specific suits also have an added loading pad on the chest, as well as some knee pads.
As for the material options, you can select between closed-cell neoprene, open-cell neoprene, and Lycra. Closed-cell neoprene suits are very popular thanks to their durability and affordable price. However, they are also somewhat constrictive and less efficient at insulating. Open-cell neoprene wetsuits are much softer and more flexible than closed cell suits. They also have greater insulating efficiency and provide an excellent range of motion. The downside is that open-cell suits are generally more fragile. Lycra suits or, as they are also called, skins are only useful in very warm water as they do not provide any form of thermal protection. They do, however, shield the diver from the sun and stinging organisms. Some skins come with loading pads for protection when loading a speargun.
Finally, you need to consider the thickness of the wetsuit. Commonly, 1-1.5mm suits are used in warm water, 3-5mm are suitable for moderate water, whereas those who will dive in cold water need a 7mm plus wetsuit. Remember though, thicker suits decrease mobility, which is so important for freedivers and spearfishermen. You may want to choose a suit that utilizes a mixture of thicknesses in order to increase insulating ability without or with minimal impact on your freedom of movement in the water.