Your kitten/cat has many needs.  Food, shelter, litter, and most importantly love.  They might need a few accessories, so make sure you are prepared for your kitten\cat.

Grooming Material

Cats are very clean animals, but for the couple times your cat needs a brushing it is worth it to buy grooming brushes.  Especially if you own older cats.  When cats become older, they have a harder time cleaning themselves.

Litter
When choosing a litter, you have a few options.  
     - fullers earth
     -chalk
     -compressed
Your cat also might want privacy, so you could consider a covered litter box.

Food 

Kittens are recommended to eat hard food to strengthen their teeth.  When they mature you also have the choice of feeding them soft food.  Water is also important.  Remember to ask your veterinarian before giving your kitten milk (because of allergies).

Toys

Kittens love to play and it is good exercise for them.  When purchasing toys, make sure they are safe for kittens to chew on.  Scratching posts are great items.  They give your kitten a place to scratch instead of ruining your furniture. 

Cats need a place of their own, like a bed, which is warm and cozy.  They like sunny spots, near a window or a vent.  But wherever it is, it has to be comfy.