If you are moving fish from an old established tank that may have different water chemistry to your home water, then take the new fish home in their old water. Use their old water to set up the tank and then do small water changes to dilute anything bad out of the tank, and to slowly acclimatise the fish to your water supply.
I have met plenty of people who bought a neglected secondhand tank with fish, took it home and put the fish into clean dechlorinated water. The fish are all dead within 24 hours due to the sudden change in water chemistry (pH, GH, KH) and water quality (ammonia, nitrite and NITRATE). I emphasise nitrate because neglected tanks regularly have high nitrate levels and a low pH. When the fish get put in water with no nitrates and a different pH, they die.
By keeping the fish in their old water for a few more weeks, and doing small (10-20%) regular (daily) water changes, you gradually improve their water quality and make it better for the fish. You do this for a few weeks and there will be less stress on the fish when you start doing bigger water changes.
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Old aquarium water does not contain beneficial filter bacteria so is pointless for setting up a new tank and hoping the old water will help with the filter cycling process.
Old aquarium water will contain a huge number and variety of harmful microscopic organisms that can harm the fish. So old water is not good if you want healthy fish.
However, for the aforementioned section about sudden changes in water quality and chemistry, old water is safer to use with a neglected tank.