I scan most of my images, because then I have no variation in the horizon vs. vertical. I confess, I use about a 12 year old photo imaging programme, not supported by Microsoft anymore, because I like the ease of use. And it works better than photoshop. I do change the background, but the immediate background around the coin, ie very close is just a similarly coloured paper I taped to the scanner lid.
I have worked with Photoshop, but whilst it is good for some stuff, I find that it does nothing for coins.