Let her pick her own, or go and pick one between you once you have proposed … its a fun process. If she is nice, she will understand your budget ( may hold back a little to keep some reserve, cause no doubt, she’ll pick something thats a little over the budget ! …. been there ! )
I say this cause I had ideas in my head of what type of ring would be the right one. Once I had proposed, we went and tried the ones I thought would be nice, and they just didn’t suit her.
Also, read up on diamonds and their grading … once you understand it, you’ll see the differences between the diamonds when you’re looking at them. Biggest is not always best.
In the end, we got a solitaire engagement ring. Not the largest, but the diamond is near flawless, near colourless and an excellent cut. It really really sparkles.
good luck.