The short answer and the reason behind it
Buy and add your fish gradually, in small groups spaced out over weeks. The reason is biological rather than cautious for its own sake: an aquarium filter is not a machine that removes waste so much as a home for bacteria that convert it, first from ammonia to nitrite, then from nitrite to far less harmful nitrate. That colony grows to match the waste it is fed. A tank cycled for a handful of fish owns a handful-of-fish colony, and it cannot instantly expand because a full community arrived on Saturday. The mismatch is what harms fish.
What happens inside the filter when you stock all at once
Every fish added begins producing ammonia immediately, through its gills and its waste, and feeding adds more. When the total outruns the colony, ammonia accumulates in the water, and ammonia burns gill tissue, suppresses immunity and can kill within days; nitrite, the intermediate stage, interferes with the blood's ability to carry oxygen. New keepers then chase the spike with emergency changes and bottled products while the fish are already damaged. The same community, added in stages, never creates the spike at all, because each stage feeds the colony just enough to grow it for the next.
A sensible stocking rhythm
Start with a properly cycled tank, then add a first group chosen for hardiness: a few fish, or one complete school of a schooling species, since a school counts as a single step rather than several. Feed lightly, test ammonia and nitrite over the following days, and wait until both hold at zero and the tank has settled, commonly a week or more, before the next group goes in. Sensitive and territorial species come later in the sequence: delicate fish benefit from a mature tank, and the boldest, most territorial additions cause least trouble when they arrive last and find the tank already claimed. Keeping notes of each stage makes the rhythm easy to follow and to adjust.
Exceptions worth knowing
Gradual does not mean splitting groups that belong together. Schooling fish should arrive as a complete school in one step, because a fragment of a school is stressed and shy, and adding the rest later can upset the pecking order the first arrivals formed. Fish sold as established pairs or bonded groups likewise travel together. A quarantine period for new arrivals, even a simple separate container setup for observation, protects the main tank far more cheaply than treating it later, and is worth the small effort for every addition after the first. These are refinements of the gradual rule, not exceptions that overturn it.
The habit that makes gradual stocking easy
Keep a stocking log: which fish arrived, when, from which shop, and how the water read in the days after. That log becomes the tank's memory, invaluable when you are deciding whether the filter is ready for the centerpiece fish, or tracing where a problem entered. A finished community built this way is healthier at every stage than one installed in a day. KinsLe's Pet Passport suits the habit well, holding each addition's details together in one portable packet alongside the tank's other records, so the whole stocking history is ready whenever a vet question, a move or a handoff needs it.