#"Intrinsic solubility"# is a bit of a nebulous term, and refers to the amount of solute that will dissolve in a given solvent. Some ad hoc rules and observations exist. Like dissolves like; i.e. polar solvents will dissolve polar solutes. Water is the universal solvent, and will dissolve most materials to some extent. Water is an an exceptionally good solvent for ionic solutes given its ability to hydrogen bond, and solvate both positive and negative ions. Of course, crystals from water probably means that you incorporate several molecules of water in the crystalline phase.
#"Temperature"# of the solvent will of course determine the extent of dissolution. Dissolution is generally a bond-breaking process, and the higher the temperature, the more solute dissolved. We use this principle in recrystallization where a solute is dissolved at an elevated temperature, filtered while hot to remove insoluble contaminants, and allowed to cool slowly so that bigger crystals deposit from solution.