Temperament
You can't predict what a kitten will be like, but an adult cat from a shelter has already shown its personality. It's a good option if you are looking for a calm animal: volunteers can tell you who the cat gets along with and what it is afraid of.
Living with a mixed-breed cat
The same rules apply as for every cat: a clean litter box, a scratching post, high perches, play, and secured windows. Cats that have lived outdoors need time: they are better off spending the first few days in one quiet room with a hiding place.
Grooming
Depends on coat length. A shorthaired cat needs brushing once a week, a longhaired one more often.
Health
Being mixed-breed does not protect a cat from disease. Every cat, especially one from the street, needs a vet exam, parasite treatment, vaccinations, tests for feline immunodeficiency virus and feline leukemia virus, and a discussion about spaying or neutering.
