Domestic Medium Hair isn't a breed. It's a coat description for mixed-ancestry house cats whose fur falls between short and long, usually with a fuller tail, tufts between the toes and a soft undercoat, but no heavy ruff. They come in every color and pattern, from tabby and tuxedo to calico and solid black.
Size, temperament and health follow the cat rather than a breed standard. Most weigh 6 to 14 pounds, live 12 to 18 years indoors, and are sturdy and adaptable, and their genetic diversity often serves them well. In Hamilton, that usually means a cat that handles an Ohio winter and a quiet household equally well. Meeting the cat is the best guide to personality.