A basic toolbox for grooming a longhaired cat should include the following:
A double-sided wire and bristle brushes is useful for general grooming. Consider a slicker brush for removing tangles, dead hair and debris. They also help to distribute healthy coat oils all over the body. A wide-toothed comb helps long hair to remain matt-and tangle-free and a de-shedding comb will keep the undercoat thinned without cutting the hair.
As with your own personal brushes and combs, it’s a good idea to regularly wash and disinfect your cat’s grooming tools. Keep them all together in a little plastic container.