Scratching post
Scratching is part of normal cat behaviour, and causes no problems when it is done outside; it's when it's done indoors that it causes most problems. The cat is actually making sure its claws are in tip-top condition through this exercise. So it's a bit more like a 'manicure' rather than just sharpening!
Scratching posts are easily bought from a pet shop, and you can even make your own, although it's not a good idea to cover it with carpet, as the cat may then think that it's acceptable to use any carpet in the house! If you place the scratching post in front of where the cat has done claw-conditioning most, it will soon use it. Once it's in regular use, move the post to a better location. To try to get a cat to use the trees outside, placing bark or a tree post in front of the scratched furniture may work. Make sure that the post is of the right height for the cat. It will need to be high enough so that the cat can stretch fully.
Cat flap
As cats are very independent, a cat flap is ideal when there is easy access to a garden. They can then come and go as they please. However, consider dealing with cats coming in from outside to eat your cat's food! If this is a potential problem, it may be worthwhile considering a 'collar-operated' cat flap, that only opens when your cat approaches.
Cat carrier
You will need to take your cat along to the vet's, and there are lots of different types of carriers available. Some cats prefer wire baskets, so they can look out and some prefer wicker ones where they feel enclosed and secure. Cardboard cat-carriers are acceptable for very short, unstressful journeys but can collapse if they get wet with urine, for example.