Cp is notoriously difficult to scan--
a sheet of acetate/drafting film *can* help to cut the glare/grainy look issue, although it may dull or mute some colors.
My scanner (this one, if anyone is curious:
CanoScan 8800F) has an LED instead of a fluorescent bulb in it, and so the light is "cleaner" (although it may run a bit coolish) and requires far less color correction/fiddling than any other scanner I've had.
The best thing I've found is to scan at the highest resolution possible, pull the image into photoshop, and save a copy that I *won't* touch so if everything goes horribly wrong I don't have to re-scan.

So then I'll adjust the contrast or color balance if needed (once you figure it out for one piece, the amount you need to adjust rarely changes too much. Unless you're scanning a piece done on black paper. Then all bets are off.

). Once I've done that, I'll reduce the size to a web-friendly 72dpi. If it still looks grainy or wrong, I'll undo the resize & apply a "blur" filter or (I know, counter-intuitive!) a "sharpen" filter. Just experimenting to hit on what looks best 'cause for this, it seems like each piece is different. Once I'm happy, I'll resize & that usually takes care of it.
If you're scanning a piece done on black or on a very dark paper, scanners will struggle to get it right. One thing that can help is putting a piece of white paper in the scanner, so just a bit of it will be picked up by the scan (you can cut it out of the image later). While it doesn't always work (depending on how finicky your scanner is), it can *help* get the contrast/colors right.
Most often, photographing does the best job. If you can get the lighting right. And the camera squared away to the piece correctly (my downfall! Can never seem to get that part right.

).
If you're scanning to create prints at home & what prints is *way* different from what you see on the screen or the original, you'll need to get the scanner, the monitor, and printer all callibrated so what info the scanner gives the monitor will also be what spits out of the printer. It's a mystical/magical/miracle laden-process I have yet to wrap my brain around.
If you haven't yet, you may also want to spend some time in the
Computers & Technology forum-- lots of good info in there!
Good luck! Looking forward to seeing some of your work soon!
Rosemary