Natural light is best, I agree. You need enough so that you can get a fast enough shutter speed to avoid blurring, though obviously cats often do
Turn the flash off though - it rarely gives good results in my experience.
To begin with maybe try when they're asleep...
But the biggest tip I can give is take the shot from cat level
- by which I mean that shots from human height of a cat down on the floor are not too interesting, mainly because you won't see much of his face only his back.
If your cat regularly sits on a chair, wall, knee etc then get down to his level as you would a human.
Ramsay on his chair:
Wide aperture used to blur his body and draw the viewer to his face.
Here by his favourite window, the red glow comes from some curtains:
Here's Hugo sitting on my friend Andrew's knee:
Blurring the background with a wide aperture i.e. a low
f number like f/2.8 is good if you can manage it - if the background is some way off it works best (not easy indoors).
If your camera doesn't have manual controls then try the macro setting.
Black and white can be nice too: