Many women prefer colored stones, such as sapphires, rubies, and emeralds. Colored stones can be set by themselves or with diamonds. A woman's engagement ring can be as expensive or inexpensive as is appropriate to the finances and wishes of the couple.
Some couples elect to have a diamond-like substitute, such as a cubic zirconia.
This is not inappropriate, and there is no reason why this choice should need to be public knowledge. Go shopping with her casually, to get an idea of what she likes, but make the final decision on your own. You may also want to take her to the jeweler even if she says she doesn't want to go, to make sure she gets to see what the other choices are. This should be done very shortly after the proposal, before she has a chance to get overly attached to the ring you gave her. Get an inexpensive ring for the proposal, and explain that it is a place holder for a ring you'll select together.