Goldfish and koi are the fish most often kept wrong, and almost always for the same reason: they are sold small and they do not stay small.
A common or comet goldfish reaches ten to twelve inches and belongs in a pond or a large tank — not a bowl, and not a ten-gallon. Fancy varieties (oranda, ryukin, fantail, ranchu) stay smaller at six to eight inches but are heavy waste producers, so they still want serious filtration and room. Goldfish are also coldwater fish; they do not need a heater, and they are genuinely unhappy at tropical temperatures.
We will say this plainly because it saves heartbreak later: koi reach two feet or more and live for decades. An indoor aquarium is a temporary home for a young koi, not a permanent one. If you do not have a pond or firm plans for one, a fancy goldfish gives you most of what you want in a fraction of the space.
Single-tailed goldfish — commons, comets, shubunkins — are fast, streamlined and will out-compete fancy varieties for food every time. Fancies are slow, and the round-bodied ones are poor swimmers. Housed together, the fancies quietly lose weight. Keep the two body types apart.
Round-bodied fancies are prone to buoyancy trouble because their organs are compressed into a shorter body. Most cases trace to food: dry flakes swallowed at the surface with a gulp of air. Soaking pellets before feeding, or using a sinking food, prevents most of it. A fasting day each week helps too.