When you first pick up your new cat - be it a kitten or an older cat - you cannot expect it to walk into your house and be immediately settled. Kittens definitely settle down quicker than older cats but you need to remember that any cat that you get will have had an established routine in another home and will now have to learn a new one.
The new cat/kitten needs time to settle into their new surroundings. During the first few weeks in your home, they should be allowed some quiet time to explore each room thoroughly. Only after they have grown accustomed to their indoor environment and have adjusted to regular feeding schedule should you allow them to venture outdoors. If you acquire a kitten during winter, you should wait for warmer weather before allowing them outside.
Whether or not your kitten should be permitted access to the outdoors is an individual decision. Although they will have more opportunity to exercise, they will almost certainly be exposed to many more dangers, such as traffic and dogs. I am a firm believer in letting cats go outside and not to be confined to the house. They are outdoor animals and hunters and need the opportunity to do what comes naturally.
Whatever your choice, you should decide early on; once a cat has been given outdoor freedom, they will not easily adapt to being confined thereafter.
It will need to learn where to find the essentials such as food, water, litter tray, cat flap and toys. It will not know which parts of the house it is allowed to explore or not - some people do not allow the cats to go in the bedrooms, for example - and finally what other pets it may face!
It may never have met another cat, let alone a dog and may not take too kindly to so many changes at once. You should also consider the existing pets, if any. Most cats do not like a newcomer being introduced to their territory and could attack them.
We had just this problem with our British Blue - Walnut. We thought it would be nice for her to have some company so we bought a 7 week old male kitten home one day and thought (rather naively) that she would be grateful for the company. Things didn't go well on the first night and all she did was hiss and spit at him. By the second night she was attacking him and we had to lock him in a separate room to protect him from her. The following day we had to take the kitten back to the people we bought him from and fortunately for us they took him back. We soon discovered that Walnut was not ready for another cat in the house!
You should remember that cats are instinctive hunters and if you have small pets such as mice, they are likely to see them as pray more than a friend. We used to keep chipmunks and had to sell them once we got the cats as it was obvious that the cats merely saw them as pray and would never get on with them.
The opposite can also occur - you may have a dog who suddenly sees the new cat in the family as his/her pray and you could find that the dog will attack the cat in much the same way as the cat would attack your cute, beloved mouse!
Supervised first meetings of the pets is essential but if you feel, like we did, that it will never work out then you should decide which pet will have to be re-homed to make way for either the established pet or the new one!
You should ask the current owners / breeders what food the kitten / cat is used to and stick to feeding that particular brand of food for a while until the cat is more settled. You can then introduce other brands of food but be careful what you feed kittens until they are older as they tend to get diarrhoea if their diet is too rich.