Whether she's a stray or a purebred, your cat requires care and attention. Just remember how you feel when you first move into a new home with new people. It's a bit like that for your new cat.
First, prepare a sleeping area for her before you bring your new cat home. She needs a warm, secure place to sleep. You can buy cat beds and baskets in pet stores. Or, you can make a bed for your new pet. Just take a cardboard box, make a cat-size entrance hole in it, and put a clean, comfy blanket inside.
Make sure the house is quiet when you bring your cat or kitten home. Don't be surprised if she seems a bit timid at first. Soon enough, she'll be overcome by curiosity. Let her settle in and explore on her own without too much interference.
It's a good idea to keep your new cat or kitten confined to the house for the first few weeks. During this time, you can familiarize her with all the normal household noises and activities. Introduce her to visitors so she becomes confident and well socialized. As for other pets, they should be introduced to the new arrival slowly and under close supervision.
You can also have a few simple toys waiting for your new cat when you bring her home. Cats are naturally playful and will appreciate these; they'll also help her feel relaxed and at ease in her new surroundings.