What is the best method and what type of doctor should I see to perform this procedure? (photos)

Both derm surgeons and plastic surgeons can do nice mole removals but a doc who has both training is truly an expert. Get those 3 moles excised and sutured nicely followed by superficial dermabrasion to help blend marks.

Surgical removal of moles, which is the  most aesthetically acceptable way to address your issue, is best performed by an experienced Facial Plastic Surgeon.  Please understand that the structures present in the facial skin, coupled with an excellent blood supply, allow for very acceptable aesthetic results in competent hands.  

This is not that complicated.  A facial plastic surgeon will be able to remove the moles safely and with minimal scarring.  You already know that any mole removal results in a scar of some type. The key is to have the scar be less visible than the mole.  This is a quick office procedure.

Benign moles do not need to be removed for medical reasons but can be removed for cosmetic reasons.  A good approach to cosmetic removal of raised benign moles is to use a shave biopsy to confirm the diagnosis and debulk the lesion and then to treat the base with a precise ablative laser such as the Truespot CO2 laser.  I have found that this successfully removes the vast majority of these lesions with minimal risk of scarring and recurrence.  You should see a board certified dermatologist or plastic surgeon who is well versed in cosmetic mole removal or you risk pigment recurrence and unsightly scarring.

Thanks for your questions and your nicely posted photos. You need to see an expert in cosmetic mole removal who is experienced in removing growths from the face. There is always a risk for scar, recurrence, pigment changes (darker/lighter/red) in the area treated, and possible need for additional procedures. But an expert should be able to remove these moles with minimal scarring and an appearance more pleasing than the moles currently. Importantly, my patients find that if the mole ares becomes flat, rather than raised, even a small scar can be easily concealed with make-up. Always you need to be diligent about avoiding the sun / proper use of sunblock for about 6 months after removal for the best results. 
Please seek out a board certified, fellowship trained Oculofacial Plastic Surgeon or other doctor with extensive expertise in cosmetic facial mole/growth removal.  I have had patients travel from around the country (USA) to have me treat them for this kind of challenging removal - especially after they were turned away by dermatologists, general plastic surgeons, and family doctors. My coordinators can conveniently arrange such a visit.  I have removed thousands of moles from around people's faces throughout my career and each presents its own challenges, risks for scar, etc. You can review my photos to explore your options -- all my results shown are unretouched, unphotoshopped photos!
Best of luck in your search.
Damon B. Chandler, MD
Harvard-Penn Trained Oculofacial Plastic Surgeon