So, I've written THREE responses on this thread, and, in an effort to be more succinct these days (an unlikely scenario, however, I am up for the challenge) I've purposefully erased every single one of my long-winded notes before posting. Honestly, there is not much to say after so many, already-offered, thoughtful, respectful and eloquent posts. There is not one piece of advice here that I wouldn't take myself.
Catia, every one here has basically hit it on the head... and I am going to bluntly drive in the nail: A diamond report alone will not help you when choosing a fancy cut diamond. You need human eyes.
I know it because I have been exactly where you are, except I did not go so far as to actually order stones for inspection. However, I DID spend hours, days actually, culling though online GIA reports hunting for cushion cut diamonds, trying to distinguish one "type" from another based on the info in the reports. I'd find a "great" report, call-up the photo, and bleh. In the end, some of the most beautiful stones (in the photos, at least) were the ones with less-than-ideal stats in their reports... diamonds that I would never have found if I'd just stuck to my original goal of looking only at diamonds with "excellent" or "very good" polish and symmetry. It turned out to be one of the most humbling, frustrating, gem experiences ever. All I learned was that one can not determine the beauty of a fancy cut diamond (or even a round brilliant, IMO) based on a diamond's recorded statistics. As OMC wrote, there are simply too many variables within each diamond. And, most importantly, there are too many important characteristics left unrecorded – need I get on my soapbox AGAIN regarding my beloved CRYSTAL...
For me, the report is back-up... the thing I check-out to understand what it is, more or less, that I am considering. For example, I like stones that face-up a little large for their size, so, a report is a place to check this out. Am I paying for weight that I can see, face-up, or is the stone heavier because it is cut very deep, making the face-up size appear smaller than one might expect for the stone's weight? I check the report. (And, despite my preference, I have knowingly purchased both extremes, btw). I like the overall look of a diamond, I want to know where the inclusions/blemishes are and what they may be. I check the report. I have a strong preference for VS-and-better stones, however, again, I have purchased diamonds with lesser clarity.
Again, ALL of this comes AFTER I see a stone that PERFORMS to my eye in a beautiful way. There is no report for a stone's crystal... ie, does the actual crystal/chemical make-up of the diamond visually remind you of kitchen glassware or the finest crystal stemware? This very characteristic makes the finest, now rare, Golconda diamonds, for example, extremely desirable. Also, there is no report for how a stone displays prismatic color... and, when you examine the diamond, are ALL the colors visible, or just a few? You may find that some colors are more easily visible than others (red can be most ticklish to see, so, of course, fine red display can be most desired).
I could go on and on... (however, I've written too much already)!