Purification of chemicals is a large branch of chemical technology, with a large number of non-universal methods. In the case of NaCl, it is sufficient to simply recrystallize it from an aqueous solution.
You can use ICP-MS for effective measurement of the purity of the sample. However, you can also use cost effective and efficient potentiometric titration apparatus for the same.
I think recrystallization of NaCl from aqueous solution may be sufficient. because the purity of the chemicals is usually determined using the physical properties of those chemicals