If your budget is 4-5K, you have quite a lot of choices. For diamonds, first consideration is carat or weight or size. If your GF's finger is small, don't need to buy so big as it will look fake. But if too small, it will also not look nice as the stone will be overshadowed by her finger . Once you know the carat, look at the market price for that size.

Then you decide the color, the whiter the better for eg D is better than H. This is so it will reflect light better and sparkles.

Next is clarity. The good thing about smaller carats is that inclusions cannot be seen even at S1 but the stone can look slightly dull. If the stone is bigger ie 0.4 and above, S1 inclusion can be seen.

The above 3Cs you can get good price at any shop, doesn't have to be a brand name shop coz you may end up paying more for the name than anything else .

But for the last C, cut, this is how a stone is cut to maximise its sparkle. There's so many types of cut advertised, most are the same. Don't be fooled by the SA. Best way is to try comparable stones with different cut at different stores. Maybe you can take pics and compare them. Usually brand name stores have better cutting, which is why the price is higher than regular gold stores.

Design also is important, a good setting can make your diamond look bigger and sparkles more.
Also you need to decide the metal holding the stone. White color, you can either go white gold (the best is 18/22K) or platinum. This is more of personal preference. Speaking as a woman who's been married for 10 years, I absolutely adore my platinum set . It still sparkles so beautifully.

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Stats: Ring from Carat Club KLCC, 0.8carat, D, VVS1, Love Diamond cut. Design 6 prong with platinum 950.