Depends on severity. For the most part, family physicians are trained to take care of simple acne-- using topical medications and oral antibiotics. But if you have acne that does not respond to routine acne medications, it's time to consider seeing a dermatologist. You family physician may not be updated on all the new advances in acne treatments (creams, pills, peels, laser treatments).
Well ... maybe. With recent advances in acne treatment, you will want someone who finds acne interesting. That can be a family doc, dermatologist or even a plastic surgeon. Call before your appointment and ask, "does the doctor like treating acne?" you deserve someone who has taken the time to keep up on the research and not just prescribe an antibiotic. Do your homework and you'll be satisfied.