It's not going to hurt anything to paint the back of the tank black or use a background from your LFS. However, once you get a reef tank established, the background is going to get covered in coraline algae anyway.
A background from your LFS is a lot easier to install and change if you don't like it. If you are going to paint it, it is best done on an empty tank. Many people use Krylon spray pant. I have also heard of people useing the plastic film used to tint auto glass.