Is there one type of doctor who will be most helpful with my claim?

Gather together, in some orderly fashion, everything from statements from employers to documents (even your own pain journal) of all situations where you find yourself unable to function as you used to. Keep track of your medication, and whether and how much they help. Keep track of all your symptoms. You will want to give this documentation to your doctor and the rheumatologist, to help them with their end of your claim, but you will also find it invaluable when you start filling out your application.