from my experience, glare is the biggest issue and the one most difficult to fix in post.
While everyone says shoot head-on, I find that to be extremely difficult to producing a good image. I use assorted diffuse lighting, no flash. I've tried polarizing filter, but not on both the lens and lighting.
What I find works best is to get even lighting by any method you can. Then I take the shot at a good angle to the painting, looking down. This minimizes glare the most. Distortion and white balance are very easy to fix in photoshop.
Typically I use a canon 10D and now a 7D, most used lens is the 50mm f1.8. Depending on the size of the painting, I may end up taking anywhere from 4 to 16 shots moving across and down the painting in rows. I'll take a "one shot" (whole painting in frame) from a pretty "head-on" angle. I use the one shot as the reference for correcting and placing the other images.
The images of the paintings are used to produce 8 x 10 to 17 x 22 inch prints for sale on assorted sites like Etsy.