I could write a few pages on the subject. The object of concern is actualy "glucose" which is the fuel your body burns, and apart from protien, which is used to maintain your muscle mass, your body is a glucose burning machine.
Usually when we use the word "sugar" we are talking about the white table variety. White table sugar generaly comes from two sources: sugar cane, and sugar beets. Brown sugar is just white sugar with some molasses added back in.

If you want a good education on sugar, start by reading The Glucose Revolution by Dr.s Brand-Miller & Wolever.

It is my experience that the easiest way to start managing your sugar is to follow a diabetic diet, or a heart diet. They are remarkably similar. Diabetics still count calories as the primary way of controlling blood sugar levels. I find that when I eat a balanced diet...which can accomodate small amounts of sugar, my dyskinesia drops out of sight. I can go two or three days with no sign of dyskinesia. Then of course my brain says lets test the limits, and sure as the sun will rise tomorrow, I'm back having trouble with my meds and dyskinesia. Radical changes in your "american" diet can help you manage your PD. But knowing is not doing, and it is tough to live in the sugar free zone. Another book that is a classic on Sugar is "Sugar Blues" written in the 70's. Amazing! But probably no longer in print. Check a used book store, or possibly a library. Don't remember the author.