I am currently a 34G. I want a Breast Reduction. What cup size would you recommend that I should aim for? (photos)

Thank you for your pictures.  In my opinion cup size does not factor in the final result.  As with any breast procedure, I try to make the breasts match the patients frame. 

Usually with large breasts the reduction will be limited by the amount of tissue required to keep the nipple areola and skin flaps alive. This is best evaluated in person but a "C" or "D" is probably possible.

Most of my breast reductions have one complaint after surgery, they all wish they had come to surgery sooner.  I believe that means most women do not go into this lightly, they think about it long and hard before they even start making inquiries.  Looking at your pictures and given the width of your breast, I think it would be difficult to get you down to a B cup and keep a pretty breast shape.  That being said, I believe the decision on what cup should be your goal is a very personal choice.  Given your body frame you would look great at a C, D or even DD,it depends on your personal aesthetic and your goals.  My job as a surgeon is to tell you what cup size I can attain and give you an attractive breast.  It's also my job to tell you that the smaller you go, the greater the likelihood your breast will stay perky in the long run.  It is not my job to ultimately choose your size.  I ask patients to bring me a bra they would like to fit into, and bring me pictures of looks they like.  That let's me get as close possible to inside your head and get you the look you desire. If your goal is to wear triangle cup bathing suits, then you probably don't want a big D.  If your wear a lot of lose fitting clothing, a larger breast can make you look thick and hide your waist.  If you wear tight clothing then you will show off your waist size no matter how large your breast.  See a plastic surgeon who is board certified with a special interest in breast.  My partner and I are just down the road in Nashville, check out our website and if you like what we do, call for an appointment.  You live in an area that actually has a great many really good plastic surgeons within close driving distance.  Choose someone well trained that you feel comfortable communicating with.  Best of luck!

Your breasts are pendulous, probably feel heavy and yes, a breast reduction will reduce the size and reshape the breasts.  You want to know about minimal scar techniques, not all plastic surgeons do this.  What you don't want is a flat breast, too small with scars in the cleavage between the breasts.    The breasts should ALWAYS be proportional to your body, you can decide if you want them a little larger or a little smaller.  I have posted some pictures of similar women on real self.

Posted photos appear as a D cup, so C cup would be attainable. But if truly a G cup than consider a D cup result... 

Congratulations on your decision to proceed with breast reduction surgery; this operation tends to be one of the most patient pleasing operations we perform.  
I would suggest that you communicate your goals clearly with your plastic surgeon (who you should choose carefully) and make sure that you have realistic expectations prior to proceeding with surgery.   Ask to see lots of examples of his/her work so you feel comfortable that he/she can achieve the outcome you are looking for. In regards to breast size desired, also communicate carefully. In my practice the use of goal pictures are helpful in this regard; a discussion of cup size can be confusing and imprecise.  For example, “C cup” or “proportionate" may mean different things to different people,  and therefore may be a source of miscommunication.    In other words, I would not suggest that you communicate your goals and/or base your satisfaction with the outcome of surgery on achieving a specific cup size.  
 I hope this, and the attached link (dedicated to breast reduction concerns) helps. Best wishes.