Q: What can I clean the screen and the back of my iPad mini with?

Here is apple's cleaning link http://support.apple.com/kb/HT3226.  I personally use a product called monster screen clean to clean all my devices.

What do you mean "about covers"?  The apple article says you should use a lint free cloth that is damp with water.  It says never apply the water directly to the device apply it to the cloth first.

I use monster screen clean to clean all my electronics.  I use it on the cases of my electronics, the keyboards, trackpads, screens, body, etc.  Works well, never damaged my devices.