Specialist. See an orthopedic shoulder specialist, who can pinpoint your problem much more readily than your regular, or family, doctor.
Good Question. Impingement syndrome as a diagnosis is increasingly controversial and i don't use it as a primary diagnosis. You can learn more about this topic here: http://www.Theshouldercenter.Com/shoulderpain/2013/shoulder-surgery/spur-acromioplasty-impingement/.
Start with PCP. Most rotator cuff problems are tendinitis, which is treated conservatively - relative rest, ice, meds for pain and physical therapy. If those treatments fail, consultation with a physiatrist or orthopedic surgeon is often helpful. An MRI is often ordered at that time. Even if the rotator cuff is torn, it might not require surgery.