Reposting this since it's come up a lot again:
Cheat sheet which is a great set of numbers for Round Brilliants. There are no set numbers for fancies.
Total depth between 59(59.5) and 61.8%
Table diameter between 53 and 57%--ideally 55-57.
Crown angle between 34.3 and 34.9 degrees -- ideally 34.5
Pavilion angle between 40.6 and 40.9 degrees --if you hit 34.5 CA you would love a 40.7 or 40.8 to go with it.
Girdle thickness between thin to medium, faceted (bruted isn't bad, but faceted is more visually appealing.)
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.
Secret sauce is a 55% table, a depth around 59.5-60%, a Crown Angle of 34.5 and a Pavilion Angle of 40.7-40.8. This will be near impossible to find through a retailer like Tiffany's.
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. When your table is on the smaller end, the stones are more fiery with more color light return than white light return, when the table is on the higher end, they are whiter (less color light return) and less fiery.
HCA scores: I do not lean on the HCA (Holloway Cut Advisor) as a final decision maker. It's a nice thing to use. Very few stones will get a 4 EX score--the secret sauce will almost certainly get you one that will though. I have seen several serious winners in the 0-2 range, and just as many dogs in the same range just as I have seen some serious winners just outside of it, and many more dogs outside of it. It is a weeder tool to help you look more closely at things. Don't hinge your bets on it.
More input on the girdle: Bruted isn't horrible, my current stone is bruted. Just about everyone will like Faceted better, but bruted isn't a horrible thing. It's not going to ruin your diamond or anything.
I tend to recommend a few specific online vendors more heavily--I vary who I go with depending what I am looking for, and for a reason: most of their stones are AGS graded with a few GIA, their stones are shown with great photography and they do extensive testing that indicates light return and proper cut quality. They also rely heavily on AGS reports, vs GIA, and AGS actually has the authority to call something IDEAL cut. They can prove it. GIA Excellent has a ridiculous margin and many stones that get that grade (or Tiffany's "triple excellent" nonsensical grade) are not actually well cut stones. There's no science behind those grades, where AGS actually has science to prove it is well cut.
Blue Nile is almost never one I recommend because they don't provide either and it's not my ideal to just buy a round on paper. You CAN, but photos and testing really help you identify a winner. I like magnified images, especially those that rotate and zoom to see the inclusions, I like ASETs and I like Idealscopes. Blue Nile does not employ those things.
