Many coin collectors take photographs on a black background. That dark background, I think, overcomes the shadows and is better at automatic exposures than a white background.
I use a gray background; the 18% grey aligns better with automatic settings than a white background, and it so happens to be very similar to the cardboard backing found on common notepads. Try that!
Whether scanner or camera, most of my effort is in post-processing, manhandling backgrounds and a coin's white balance in a photo editor. With respect to the background, all I want to do is to make it as uniform as possible, which makes it easier to select and remove in a photo editor.
I upgraded from scanner to camera (a smallish Micro 4/3rds format, with a long macro lens) over 10 years ago. While the scanner was
good, it was never great, and it could not offer much depth of
field (more of a problem with
Greek coins than
Roman).