The Carat
Notice that I put this as the last consideration of all the Cs. Reason is simple. Once you have determined the Cut, Colour and Clarity that you want, it will be relatively easy to find the carat weight of diamond that suits you and your budget.
Important to note is that a 2-carat diamond does not mean twice the size of a 1-carat diamond when viewed from the top. The cost, however, will always be more than twice the cost of the 1-carat, assuming the same quality.