What are the cations and anions whose compounds are usually soluble?

Answer: -

Solubility of a substance depend on the balance of intermolecular forces between the solvent and solute, and the entropy change that accompanies this process.

Temperature and pressure also plays a role in solubility.

A solution having Group 1 cations like lithium, sodium, potassium etc are always soluble.

A solution having NH₄⁺ is soluble.

All salts with anion as nitrates, acetates, chlorates, and perchlorates are soluble in water.