The right camera depends upon how much you know about photography.
You will be shooting in close focus or Macro mode depending upon the distance you are from the painting.
If you are planning to use the camera in Auto Mode only, then most digital cameras will do.
The Panasonic ZS15 has very good auto white balance and should give you true colors plus excellent picture quality. It sells for a bit over $200 USA.
If you are accustom to using a camera that lets you take charge in manual mode,
I would look at the Canon G12.
It sells for about $450 USA.
For shooting paintings you want to use a focal length that will not distort the image.
About 50mm is ideal. (50mm is neutral - no wide angle and no zoom).
Most newer model cameras have gone to wide angle lenses (about 25mm).
That should not be used at the normal setting.
To compensate, you need to add some optical zoom (about 2X) to set the focal length to approximately 50mm.