Why water composition matters at all
Brewing tea is extraction, and what dissolves out of the leaf depends partly on what is already dissolved in the water. Water with a moderate mineral content extracts more of some compounds and less of others than very soft or very hard water does. This is why the same tea can taste noticeably different in two cities, and why traditional accounts of tea regions often mention the local spring water.
The practical version
Very hard water flattens tea, dulling aroma and often leaving a film on the surface of the cup. Very soft or distilled water tends to give a thin, hollow result, because there is nothing for the extraction to work with. Moderately soft filtered tap water is the practical sweet spot for most people in most places. If your tap water is heavily chlorinated, a simple carbon filter jug removes the chlorine taste and costs very little; that is usually the single biggest available improvement.
Freshly drawn, and not re-boiled
Water holds dissolved gases, and boiling drives them off. Water that has been boiled, cooled and boiled again is measurably flatter, and the difference is perceptible in delicate teas. Draw fresh water each time and boil it once. This is a small effect and an easy one to capture.
What is not worth doing
Buying bottled mineral water specifically for tea rarely justifies its cost or its packaging, and the mineral content varies enough between brands that the result is unpredictable. Distilled or reverse-osmosis water makes tea worse rather than purer. Elaborate remineralisation recipes exist and belong to a small enthusiast niche; nobody needs them to make good tea. Filtered tap water, freshly drawn, at the right temperature, covers almost every case.