-Light return will be round, always. There are some fancies cut with more defined optics now, but a well cut round will always do it.
-However for color saturation you usually want a pear, cushion or radiant, bec they're cut to retain color vs return light for a round. If you can avoid a round for a fancy those are not really cut for color retention, they're cut for light return.
-Visual size per carat: round OR elongated fancies like pear, marquise and emerald cuts
-As far as numbers: the only cut that has defined numbers for cut quality is Round. Princess kinda does, but not like a Round. Princesses vary a little, they're deeper generally with steeper angles. The rest are a "choose by the ASET and with your eyes" kinda thing.
Cheat sheet which is a great set of numbers for Round Brilliants
And I’d ask the sales person to limit the selection of round brilliant cut diamonds which they offer to me so that all of the diamonds are within the following range of proportions:
Total depth between 59 – 61.8%
Table diameter between 53 – 57%
Crown angle between 34.3 – 34.9 degrees
Pavilion angle between 40.6 – 40.9 degrees
Girdle thickness between thin to medium, faceted (bruted isn't bad, but faceted would be better)
Culet size: none
When you're dealing with a table of 53-54, you want the depth to be in the 59-60 range, not the 61-62 range. I harp on the 55 because it's RIGHT in the middle of the range, and sometimes a 56. The middle of the range is PERFECT, and is always talked about as the perfect table number.
The angles mentioned in degrees are a range, obviously you're going to have interplay, so there's not a specific ratio there. You have to see what the numbers on each stone are. There really is a bigger range of angles than that but ideally those would be great to hit.
Girdle: Bruted isn't horrible, my current stone is bruted. I LIKE Faceted better, but bruted isn't a horrible thing.