Silicone CCs in order to go from a small B to full C cup? I'm about 5'3", 120lbs. (Photo)

Thank you for the question and picture. Based on the photograph, you are starting at a good place and should have a very nice outcome with breast augmentation surgery. There is no accurate correlation between size of breast implant and cup size achieved.
Generally speaking, the best online advice I can give to ladies who are considering  breast augmentation surgery ( regarding breast implant size/profile selection) is:
1. Concentrate on choosing your plastic surgeon carefully.  Concentrate on appropriate training, certification, and the ability of the plastic surgeon to achieve the results you are looking for. Ask to see lots of examples of his/her work.
2. Have a full discussion and communication regarding your desired goals  with your plastic surgeon. This communication will be critical in determining  breast implant size/type/profile will most likely help achieve your goals. 
In my practice, the use of photographs of “goal” pictures (and breasts that are too big or too small) is very helpful. I have found that the use of words such as  “natural” or "full C cup”  etc means different things to different people and therefore prove unhelpful.
 Also, as you know, cup size varies depending on him who makes the bra; therefore, discussing desired cup  size may also be inaccurate. Again, best not to discuss your goals and/or judge the outcome of the procedure performed based on achieving a specific cup size.
 The use of computer imaging technology may also be very helpful during this communication process.
3.  Once you feel you have communicated your goals clearly,  allow your plastic surgeon to use his/her years of experience/judgment to choose the breast implant size/profile that will best meet your goals.  Again, in my practice, this decision is usually made during surgery. I generally select appropriate breast implant size/profile after the use of temporary intraoperative sizers and viewing the patient's chest in the upright and supine positions.
I hope this (and the attached link) helps.

Over the internet we can ONLY guess. I pick a 350 cc UHP. But best to seek IN PERSON opinions from the over 80 boarded PSs in South Florida...