Educate yourself regarding the 4Cs (cut, colour, clarity, caratweight) and spend some time reading about what is more/less important (unless you're independently wealthy, there will be tradeoffs, so you need to know where they can be made). Also, get recommendations from friends who've just gone through the process and then shop around a bit on your own before going with your girlfriend.
Good luck!
Shop the stone and only buy from a reputable source. If you buy a large stone, buy a good one and insure it. The rise in price for larger stones is not linear. Larger stones are not as common and therefore command a higher price. For $15k you should be able to get a reasonable good stone larger than 2 carats. Of course, if you went with Zircon you could get the same size stone for about $100.
I've known of women that asked for a 3 carat stone and actually received one only to determine that it was too big.