Is there anything else that is important in choosing a diamond?

• Absolutely! First of all, a diamond should be accompanied by one of the world's leading grading reports: e.g. The HRD or IGI in Antwerp and the USA-based GIA or AGS.
• Diamond grading reports are granted for a fee by independent gemology institutes (e.g. GIA, HRD, IGI, AGS). The most important thing about these laboratories is the fact they are impartial in their examination (yet, not all are impartial, unfortunately!). This ensures the stone will get the true grade if the grader sees fit to give it. Some other grading reports (e.g. EGL) may be less accurate.
• You should inform yourself about the priorities you set to your diamond's budget. Do you prefer colour to clarity? Do you prefer size to colour and clarity or will you go for the very top?
  In any case, and I cannot emphasize this enough, the cut should be perfect to near perfect!
  The reason is simple: cut is what you see in the sparkle!
  I would even go as far as to state that it is sometimes better to buy a lower quality colour or clarity diamond with a perfect cut than to buy a higher quality colour or clarity gem with a poor cut.
• I strongly recommend NOT to buy any carat weight that ends in .00 such as 1.00ct or 2.00ct.
  We, the diamond traders look at these stones with suspicion because most of the times the polisher has had instructions to do whatever necessary to keep the stone from becoming 0.99 or 1.99 ct.
  I have seen many diamonds that still had a bit unpolished (rough) just to maintain the commercially interesting 1.00 carat or 2.00 carat weight!
• Fluorescence. Diamonds can glow in ultraviolet light - have fluorescence - and even though I prefer 'none' to 'slight', this is not an obstacle for me when I purchase my diamonds.
  "Medium" to "Strong" fluorescence will make your diamond appear "overblue" - such diamonds used to be prized in the past as the best diamond colour D is a "Blue white". You should be careful to inspect the diamond first as sometimes "Strong" fluorescence can cause the diamond to appear milky white/hazy in daylight. However, medium fluorescence diamonds may be a good purchase if you like your diamonds to be overblue as this will make any diamond face-up whiter. This is a particular advantage for diamond of colour I (slightly offwhite) and below. Here is a summary from GIA study on this subject :

  "Some gem diamonds fluoresce, most commonly blue, to the concentrated long-wave ultraviolet radiation of a UV lamp. There is a perception in the trade that this fluorescence has a negative effect on the overall appearance of such a diamond. Visual observation experiments were conducted to study this relationship. Four sets of very similar round brilliant diamonds, covering the color range from colorless to faint yellow,

  were selected for the different commonly encountered strengths of blue fluorescence they represented. These diamonds were then observed by trained graders, trade professionals, and average observers in various stone positions and lighting environments. For the average observer, meant to represent the jewelry buying public, no systematic effects of fluorescence were detected. Even the experienced observers did not consistently agree on the effects of fluorescence from one stone to the next. In general, the results revealed that strongly blue fluorescent diamonds were perceived to have a better color appearance when viewed table-up, with no discernible trend table-down. Most observers saw no relationship between fluorescence and transparency." For more information see http://www.gia.edu/pdfs/W97_fluoresce.pdf which is the results of GIA research on this subject.

For further information see Diamonds Glossary.