It's all about proportions and ratios. Just make sure that while maximizing the face and reducing depth...it's not done at the expense of proper ratios for reflection and refraction (which would affect the sparkle), and potentially make the stone look more glassy. Read up on the proper ratios for your particular cut (table, crown, girdle, pavilion, depth, etc.). That should at least give you a good indication on it's potential. Otherwise as 909 mentioned, the brilliancescope data will show you the amount of light leakage as well. But ultimately it's best to see the stone in person in the proper environment. Beware the use of overly bright halogen spotlights in the ceiling as that would make it look much more sparkly than it actually is. A more neutral lighting or if you can see it in natural sun light would be good.
Another trick to make the stone look larger is to mount the solitare on a high prong setting. This will make the almost the entire stone visible, occupying more visual space.
I ended up getting a custom X-prong that looks like the Tiffany Lucida by a jewler that formerly worked for Tiffany's. While a very cool and elegant setting, it buries a large part of the stone behind the cross bars, making the stone smaller looking than it is, which is kind of a shame. But my GF said she liked that, as it's less ostentatious.
Also if you are going to order on-line, you'll probably want a GIA certified stone for some peace of mind. Though if it's from a reliable source, you may get one that has not been certified for some savings (at least $75).
But definitely spend some time on pricescope to familiarize yourself with the terms and things to look for. Use the Multi-Vendor Diamond Price Comparison on their home page to get an idea of pricing for a particular combination of CT, Color, Clarity. That will likely be about as competitive of pricing as you are likely to see. If you can get your hands on a Rappaport Report, that'll also give you an idea of the general pricing based on a grid.
Based on the prices I got off of the Price Comparison, I was able to put together my own pricing grid (color/clarity grades). You can do this for diamond sized up to .5 CT and from .5 CT to 1 CT. Diamonds are priced based at these particulary cutoffs and prices jump from say .49 to .51 as a result. This will give you a better idea of what color/clarity combo will fit your particular budget at a given size.
I must have looked at dozens of stones and closely inspected about 2 dozen before finding the right one...like the girl, you'll just know.
Other secondary things, besides the 4 C's, to look for are:
Girdle (edge of the stone): I should be around thin/medium as too thin will make the edge of the stone fragile and potentially chip and too thick will be wasted carats as well as affecting the reflection/refaction.
Culet (point of the stone): Try to get a stone with no culet as a large culet allows for light leakage at the bottom of the stone.
Florescence: Here in the U.S. people heavily prefer no florescence as it's more representative of the purity of the relationship. Elsewhere people may prefer florescence as the stone may appear brighter in lower lighting.
Polish: Generally good to get EX for polish as it'll make the stone look shinier.
Symmetry: Again, try to get EX as who wants a lopsided stone?
Table (a ratio of table to face): I wanted a radiant cut which should have a ratio in the 60's. You'll have to check for the ideal for your particular cut.
Depth (a ratio of table to depth): Again for a radiant cut, it is ideal to keep in the mid-60's. You'll have to check for the ideal for your particular cut.
Also If your GF wants a rectangular stone, then you should also focus on the length to width ratio. L = W if she wants a perfectly square stone. My task was made more difficult because I wanted a ratio of about 1.25x.
After 3 months, I found a Radiant that was D, VS1, no culet, no florescence, medium/thick girdle, EX polish, EX symmetry, 68% table, 64% depth, 1.23 ratio. Also this particular stone had a very nice distribution of facets. Since this stone was also sold directly by the cutter, it was priced much less than comparable stones that have been brokered and traded.
