What culture medium should we use for tap/drinking water bacteria?
Usually when culture-based methods are used to test drinking water a range of selective culture media are used (media that favor the growth of a specific category of bacteria, e.g. the MacConkey Agar mentioned in the article you linked to). This is because the aim is to test for the presence of known harmful bacteria.

I would suggest that any of your suggestions (LB agar, Nutrient Agar or Tryptic Soy Agar) would work just fine.

On another note: How are you inoculating the agar? The concentration of bacterial cells in tap water is very low, to test for bacteria usually a large volume (~ 1 liter) is passed through sterile filter paper which is then pressed onto an agar plate to transfer the bacteria.