Carat:

Once you have figured out the Cut, Color and Clarity the Carat is the budget breaker.

It is important to understand that when you compare two diamonds of the same shape, the one having a larger carat weight does not always translate to the larger looking stone. Delicate fingers (ie. Boney or thin and long fingers) will make the diamond engagement ring look bigger. Thick fingers will make a diamond disappear. Consider a cluster of smaller diamonds.

Some Points to Consider:

If your recipient is very active or not used to wearing jewelry, she may find herself bumping or nicking her new ring. Consider a smaller size diamond or a setting that protects a larger diamond from getting knocked against doors and counters.
Also keep in mind that the smaller the finger, the larger the diamond will appear. A 1½-carat diamond solitaire looks much larger on a size 4 finger than a size 8.
If you have already chosen a setting, make sure you choose a diamond to fit. Look for the diamond size specifications of your ring.
Finally, if a large carat weight is important to you, yet you're working within a budget, consider a diamond with a good cut, SI1–SI2 clarity, and an I or J color grade