You should ideally use natural spring or mountain water. This isn't always practical, and most US and European tap water is acceptable. There are benefits to be had from filtering your water; those living in large cities or in places where the water tastes strong and unpleasant -or if the water is especially hard - then filtering it is vital.
When filling your kettle, only use the water you will need for each infusion. A very important factor in preparing a good cup of tea is having oxygenated water. Each time you boil the water the amount of oxygen is reduced. Freshly boiled new water will contain more oxygen and should give you a brighter cup of tea.