Various surgeons. A blepharoplasty can be performed by various surgeons who are equally qualified. There are various ways to perform a blepharoplasty. It is more important to determine what type of blepharoplasty is ideal for your problem and if other surgical procedures are indicated (brow or levator procedures). See a facial plastic surgeon for consultation.
Do your homework. As with any cosmetic surgery, do your homework. Look at on line reviews -/+. Ask other patients. Cosmetic surgery is both art and science; but art is most important. Look at before and after images. Certification, experience can guide you in your decision. Choose well. Most can get a driver's license, yet not everyone can drive. Certification is important, but experience and outcomes are more..
Many are the best . There are many well qualified, experienced blepharoplasty surgeons. Singling a single person out as "best" is subjective at best.
Oculoplastic surgeon. Oculoplastic surgeons are specialised in eyelid surgery therefore all aspect of your eye and eyelid conditions are considered prior and during the blepharoplasty to avoid complications.
Depends on goals. If your goal is purely aesthetic improvement, a board certified plastic surgeon is the best type of surgeon available. They had an early interest in the art of aesthetics, and pursued it their entire training and career. It is their only focus. If, however, you have a functional eyelid issue, an ophthalmic surgeon is preferable, especially one experienced in eyelid surgery.