Domestic Short Hairs, i.e. moggies, are usually born in summer so you may have to wait until then for a kitten. Local papers often have them available in the "Classified" section.
Many cats present themselves at the back door and ask to be taken in. It may be a good idea to take them to a vet and discuss their health, etc.
The Petcare Information Service (Phone 1800 631 784 or see the Pet Net Website) offers an advisory service called 'Select a Cat' to suggest breeds that will suit your lifestyle. It can provide the history and profiles of many breeds.
The list of breed secretaries who may know of currently available litters is given out by the Cat Fanciers Society.
Be warned that some breeds have genetic faults, eg rolled in eyelids, squashed in noses, whilst others have unpleasant characteristics, eg vocalisations that you may hate, coats that require daily brushing for the next 15 years, etc.
Be warned also that many catteries carry virus diseases that can pass from one generation to the next. Diseases to be considered are Feline Infectious Peritonitis, Feline Leukaemia Virus, Feline Herpesvirus and Feline Calicivirus. Buying a cat with a certificate of vaccination is no guarantee of freedom - they can be infected as young kittens before vaccination time.