A good place to start is looking into exactly what conditions are required for each salt to dissolve completely into solution (meaning proper ion separation, not just "you can't see it any more") and go from there.
That shouldn't take much effort:
Calcium Carbonate: Insoluble. Shouldn't be used
Sodium Carbonate: Infinitely soluble*. Shouldn't be used
Calcium Chloride: Infinitely soluble
Calcium Sulfate: Soluble to the extent of 2 g/L at 20 °C. More soluble in cold water
Magnesium Sulfate: Infinitely soluble
Sodium Chloride: Infinitely soluble
Potassium Chloride: Infiinitely soluble
Calcium Hydroxide: Soluble to the extent of 1.73 g/L at 20 °C. More soluble in cold water than hot. Use vary sparingly and only if required.
*Infinitely soluble in this context means that as much as you would ever want to dissolve in a brewing situation readily dissolves.
Calcium carbonate should not be used because it does not dissolve unless acid is added and it raises alkalinity
Sodium carbonate should not be used because it raises alkalinity and because it will cause stripping of calcium when a solution containing it which also contains a calcium salt is heated (precipitation of calcium carbonate).