Within your given budget:

Cut is the most important because it determines how much sparkle/fire the diamond has. Always go for GIA triple excellent (or the equivalent).

Second important is Size (i.e. Carat).

Color and Clarity you can skimp a bit because vast majority of people with untrained eye won't notice the difference between an I/J or an F diamond. They also won't be carrying around a 10x loupe.

Whatever diamond you choose, make sure it is reputably certified. In-house certifications are rubbish and to be avoided at all costs.

If you want to get an indication whether a shop is overcharging you for the diamond, look up reference prices on bluenile.com

10k won't get you a decent sized rock in t&c, you'd need to top up a huge amount.

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Added on July 30, 2012, 1:44 pm
I would be very hesitant to buy anything that isn't certifed by one of the top agencies, GIA, AGS, IGI, etc.

The problem with other certifications is that they don't necessarily have the same standards. In-house certification is the worst one, cos they can whack whatever they want.

I learnt this the hard way with my first purchase, an SK jewelry Cellistar range diamond. The in-house cert said it was "near colorless," so I assumed it was G-J equivalent on the GIA scale. Guess what, when I go and compare with other proper diamonds, it was very obviously yellow. But when I tried to fight I didn't get anywhere because SK never anywhere claimed that their "near colorless" was following the GIA scale (or AGS scale, etc). They just said "according to our in house certification standards this is near colorless," and you're screwed.

[edit] Another thing which may or may not be a consideration for you. If you ever want to sell off your ring in the future, pawn shops will not take your diamond if it doesn't have a GIA/AGS/IGI/etc cert.

this one you will need to decide for yourself what looks "better." For me, personally, I prefer the "standard" 58 facet. any more than that and the diamond becomes to "busy" for my eye. I saw a 221-facet diamond before and honestly it just looks like crap cos there's no more "obivious"/large sparkles, it's just one huge mess of too many miniscule ones.