Sodium chloride (\( \text{NaCl} \)) is an ionic compound that dissolves easily in water due to the strong ion-dipole interactions between its ions and water molecules. In contrast, \( \text{CaSO}_4 \), \( \text{BaSO}_4 \), and \( \text{AgCl} \) have much lower solubility in water, with \( \text{BaSO}_4 \) and \( \text{AgCl} \) being nearly insoluble.
Therefore, the most soluble compound in water is \( \text{NaCl} \), corresponding to option (1).