AGS have introduced "ideal" proportion gradng for princess cuts, and they will include more fancies as soon as they can.
Long narrow diamonds, like marquise, pear and oval diamonds, often have a dark "bow-tie" effect near the center of the stone.
Some popular length to width ratios: marquise 2:1, heart 1:1, princess 1:1 (square) and emerald cut 1.5:1, but your personal preference might be longer or shorter.
Watch out for very thick girdles that result in paying for excessive weight. And be wary of thin girdles at the critical pointy ends of princess, marquise, hearts and pear shapes.
It is very easy to see inclusions and lower colour in emerald cut diamonds because they have a less "cluttered" look. The end facets are often cut too steeply and can look very different to the side facets, it is better if they look similar. The keel length, or long culet, should be about the same length as the difference between the stones length and width.
Grading the Cut of fancy shaped diamonds is complex. Pricescope helps with on-line selections here, but it is best to see and compare non-round diamonds in person. The Fancy Cut Grading system developed by D. S. Atlas‘ lab Accredited Gem Appraisers (AGA) gives parameter advice that is useful for rejecting fancy shaped diamonds with poor spread or durability risks etc.
There are many patented and branded new diamond cuts; most are marketing gimmicks, a few perform very well. See also
Proprietary Diamond Cuts
Fancy shaped diamonds – not as brilliant