Maybe for ADR it would be little better to go for orthopedic surgeon.
Personally for most often procedures like discectomy I prefer neurosurgeon as I think their training and education during their college is different, and in my opinion better, than in orthopedists.
But, after normal education at college, booth neurosurgeons and orthopedic surgeons who want to work with spine patients specialize in spinal surgery. In my country, all leading spinal surgeons are neurosurgeons, but if I noted correctly, in USA situation is completely different and leading names are mostly orthopedists.
I suggest that you read:
Neurosurgeon or Orthopedic Surgeon? Does it Matter