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While there are many readily available kits in the commercial market for testing the type of minerals present in water,
I am ready to spend some bucks on raw materials, if I can get the knowledge of how to build such apparatus
This probably not what you are looking for, but the cheapest and least time-consuming analysis is the one done by others for free.
Over here (Germany), local water suppliers are required by law (Trinkwasserverordnung - TrinkwV) to monitor the quality of potable water. This includes a large number of microbiological and chemical parameters. The details are given in the annexes 1-5 of the TrinkwV.
The results are published and are are available online at no cost.
Examples (mostly in German) are:
