If initial symptoms such as Depression or Anxiety happens, who should I seek treatment from first, a Neurologist or Psychiatrist?

That is a very good question. If the anxiety or depression symptoms are because of Parkinson's Disease, I would suggest the person to sees a specialist in Parkinson's Disease first, because sometimes optimizing the medication helps with symptoms of anxiety, so when the Parkinson's Disease is better controlled the anxiety improves.

I also want to mention that in some patients where the medication is optimised but the patients have very severe anxiety attacks, it can feel like someone is sitting on the chest and they are unable to breathe, it is a very strong and uncomfortable sensation, we have done DBS on these patients and those symptoms have gone away.