Digital should work fine, but the key is lighting. What you want to do is get two of the same kind of light, say, two quartz halogen lights from a hardware store. Set one up on each side of the artwork, at a 45 degree angle to the surface of the art. This will prevent reflections from bouncing off the painting and getting into your photo. Then you want to set your white balance to "incandescent" to match the light from these lamps. You may also want to use a polarizing filter to further knock down reflections that may come from the little bumps of paint.
Then use a steady tripod, and stop down to about f/8 on your lens (this will produce the sharpest results) and ISO100 (for the least digital noise). You'll want to be in manual mode for all of this, by the way. Set your shutter speed to give you the best image quality - it will probably be fairly slow like 1/8th or 1/4th second. Use the self-timer function to remove any vibration from the camera before the exposure.
If you have a macro mode on your camera or a macro lens (in the case of a digital SLR), use that. It will give you the best detail for something this close to the camera. You want to almost fill the frame to get the best detail, and use the highest quality setting, like L and "Fine" or, if you can, use RAW. You'll also want to be very careful that the camera is parallel to the piece of art, and level with it.
If you do plan to use a film camera, you can use the exact same lighting setup described above. The film you'll want will be something like Ektachrome 160T, which is balanced for tungsten (incandescent) light sources. Everything else described above would be the same, i.e. camera position, using a macro lens, using a steady tripod, using manual exposure, and self timer.
Good luck!