The animal kingdom is divided into those animals which have backbones, vertebrates, and those animals which do not have backbones, invertebrates. In terms of the numbers of animals which have ever lived throughout the history of the Earth, the invertebrates are much more common. Many invertebrates had external shells made of chalk-like materials to protect them. Others had internal skeletons made of similar substances.
Therefore, you are most likely to find fossile of animals which were numerically common, widely distributed, possessed hard parts, and which lived in conditions suitable for their preservation. In other words you are most likely to find fossil invertebrates.