VVS or VS. S will not sparkle enough. Jewelers put multiple spot lights in the ceiling to get lower grade diamonds to sparkle.
Color with no visible yellow. You can go slightly yellow if you follow the advice below.
Round cut (more sparkle than any other cut)
Carat at least 1.25 or better
GIA certified
Don't fall in love with a diamond because of how it is mounted. Pick the diamond and have it mounted in whatever she likes.
I bought my wife's first diamond from Antwerp, Belgium. The anniversary diamond I bought from a cutter in Tel Aviv and had it mounted in Nashville.
If you buy a yellowish diamond, mount it on yellow gold with green emeralds on either side to offset the yellow of the stone. If your fiancee wants a white gold mount, you can't go with any noticeable yellow.
Get the diamond first. You can have it mounted in whatever you like later or have it remounted for an anniversary present.
If you're close to Nashville, there are some decent jewelers there because there is so much wealth in Nashville. Salem Emamalie at Brentwood Jewelry is an old world craftsman who mounted our 2nd ring. I'd recommend him. It is one of a kind... 3.43 carats with 8 emeralds in decreasing size on the band. There are other reputable jewelers in Nashville. If you're going to pay over $5,000, then traveling to a city with direct buyers in the diamond market will be worth your while. (Obviously, my wife's anniversary diamond cost quite a bit more than that.)