How many cc for full C Cup?

Patients often think in terms of cup size when considering augmentation. Unfortunately, devices are sized in terms of milliliters (cc) of volume. This can lead to some confusion when sizing. Additionally, it is important to remember that cup size itself is not standardized with variations from one manufacturer to another. Unfortunately, as many women can attest their cup size in an industry leader such as VS is not necessarily transferable to another brand.
Another point which is often under appreciated is that of anatomy and starting point. Any implant will add volume to the volume which is already present. The implant is additive. A particular volume will not necessarily confer the same cup size to different patients (often times it will not even confer the same cup size to different breasts in the same individual...remember they are "sisters" not "twins"). 
A general rule of thumb is that 125cc can represent somewhere between 1/2 to a full cup size increase. Smaller volume differentials (25-50cc) are typically less consequential representing a volume change of less than a shot glass. However, I have found these numbers, at least anecdotally, to be of little help. Patients often present with notions/goals which do not correlate with these sorts of sterile volumetric assessments.
When sizing patients, there are a number of useful tools including:
-3D imaging (has the added benefit of offering a volumetric analysis of the pre-operative breast)
-Breast sizers (rice bags)
-Goal photos
I also recommend that patients commit to a particular look rather than a cup size. Once a patient settles on a look that pleases them the overall cup size increase becomes less relevant.With regards to your specific question, you appear to be an excellent candidate for augmentation. Your choice of a high profile device is reasonable (as you appear to have an narrow frame). The operative word for you is "conservative." Trying to be too aggressive or exceeding your native BWD is more likely to yield the dreaded "fake" look.As always, discuss your concerns with a board certified plastic surgeon (ABPS).

Without a physical examination it is difficult to respond with accuracy, but the best way to determine which breast implant type and size is best for you is by first finding out your specific wishes not only with words or letters as in cup size or “not too big” or “natural”, but also with a visual understanding of what you hope to look like. This can be accomplished either with photographs of patients whose breasts and body type look like you, or ideally with photos of patients not only whose breasts are similar to yours, but are also a similar height, weight, and pre-operative breast size. In our own practice we have provided that unique functionality on our website to accomplish exactly that. 

Unfortunately the most common reason for a woman to be unhappy after her augmentation is feeling as though she is either too big or not big enough. Thankfully, in our practice this is rarely a problem because implant size selection is what we spend most of our time discussing and determining. I do not place the onus of selecting the breast implant size on my patients since they are coming to me for my advice and expertise, but I do ask my patients to be as specific as possible about their aesthetic goals and I then advise them accordingly.

Implants vary in width, projection and volume. This can be very confusing to women, who are used to discussing one number only such as “300 cc’s”. To better understand which implant is best for you, in our consultation room we have two shelves one above the other, each with four implants.  The top shelf has all the implants with exactly the same width (12.5 cm), yet the less projecting implant with that width is a 275 cc Moderate or Classic, and the most projecting is a 590 cc Ultra High Profile. On the lower shelf, all of the implants are 300 cc implants, yet the less projecting implant has a width or diameter of 12.8 cm, and the most projecting of the 300 cc implants is the Ultra High Profile which has a 9.7 cm diameter. The IDEAL Structured Saline Implant is an excellent option that has recently become available as well. 
Once it is determined which implant type, and which width or diameter would best fit you, the next step is to decide which what sort of look you are hoping to achieve, i.e. more projection, moderate, or least. This is determined by how much breast tissue you have naturally, and how large you ultimately wish to be. All of this would be discussed during your consultation. And don’t be shy about coming prepared with images which you feel best represent your desired end point. These can be determined by visiting our gallery, or any other photos you wish to bring. The advantage of using our gallery is that all of the relevant information about patient age, implant size and type, are clearly indicated. 

I would advise you to seek the advice of a board certified plastic surgeon experienced in breast enhancement surgery and make sure that your own sense of aesthetics aligns with that of your plastic surgeon. Your idea of “natural” or “pretty” or “proportionate” might be different from your plastic surgeon’s and it is very important for you to feel confident that you are both of like minds as far as the goals. Best of luck to you and I hope you are successful in achieving the enhancement you are seeking.