I don't think 350 to 375 cc will get you to a solid D, but more than likely will get you to a large C cup. It's tough to say without seeing you but I would probably recommend about 450 cc based on your description. Good luck!
There is no way to guarantee cup size. Bra sizing varies greatly from brand to brand. A C in one brand could easily be a B or D in another. Without pics or measurements, it is especially difficult to determine in your case.