Why shape can come first
Shape is the outline of the stone seen face up, and choosing it narrows much of what follows, including the setting and the proportions worth looking at.
You may find you have a preference before you can explain it. That is fine — the explanation can come afterwards.
Educational illustrations — not items offered for sale.
Round
The standard round brilliant is currently the only shape that receives an overall cut grade on GIA reports. Every other outline counts as a fancy shape, and fancy shapes receive no overall cut grade there, so there is no single cut grade to compare across every shape.
Elongated shapes: oval, marquise, pear
These stretch the outline in one direction. Set lengthwise in a ring, the stone extends along the finger.
They can show a darker band across the centre, sometimes called a bow-tie. It varies from stone to stone — narrow or broad, faint or dark, persistent or lightening as the stone moves. In GIA research on oval, pear and marquise diamonds, observers generally disliked a bow-tie that was broad, dark or persistent, and their opinions differed as it became narrower, fainter or lighter with movement. Whether a particular one bothers you is something only looking will settle.
Step cuts: emerald and Asscher
Instead of many small facets, these have rows of four-sided facets running parallel to the outline, like steps.
Because those facets are larger and more open, step cuts can show inclusions and body colour more readily than brilliant-style cuts.
Cushion, princess, radiant, heart
Cushion has a square or rectangular outline with rounded corners. Princess has a square outline and a brilliant-style facet arrangement, and is sometimes called a square modified brilliant. Radiant has a square or rectangular outline with cropped corners, and a brilliant-style facet arrangement too. Heart depends heavily on symmetry: its two halves should match.
Two stones of the same shape and weight can still look quite different. Comparing them side by side, under the same light, is a practical way to see the difference for yourself.