First, according to the coat/hair/fur pattern/colour. Put your file in one of these subcategories. ONLY if you can't find an appropriate category, put it in this category (Category:Felis silvestris catus).
Use these categories for predominantly one-coloured cats ("solid" or "self"):
Second, according to breed. If your cat is a purebred, put it in the appropriate subcategory of Category:Cat breeds. If it is no identifiable breed, it can be put in Category:Domestic cats, but this is optional.
Third, according to hair length. If your cat has long hair, put it in Category:Long-haired cats. Medium length and short-haired cats are the most common, so they don't have separate categories. If your cat is hairless, it probably belongs in Category:Sphynx (cat) (a hairless breed).
Fifth, what does the photograph show of your cat? Is it a photograph of the cat's face? Then put it in Category:Cat portraits. Does it show some distinct body part of the cat? Then put it in Category:Cat anatomy. Does it show the cat doing something interesting or unusual, something other than just sitting there? Then put it in Category:Cat behavior.
Sixth, what does the photograph show besides the cat? Is it a photograph of a cat in snow or autumn leaves? Does it show the cat on a fence, in a tree, or on a wall? Then put it in Category:Cats by setting.
Anytime you don't know how to categorise your photo, just put it in this category directly, and someone else will subcategorise it for you.