While you can certainly just bring a cat home, a little planning can go a long way if the new cat is your first cat in the house. If it is a planned event to bring a cat home and not an impromptu rescue (or other random situation), then make an appointment with a veterinarian that coincides with bringing the kitty home.
Once your new feline friend has a clean bill of health, bring them home and prepare to do a little shopping if you don't already have the necessities; cat collar, ID tags, food, food/water bowls, treats, toys, litter box/litter, scratchers, grooming supplies, and so forth.
If you have never had a cat, it's difficult to fathom the trouble they can find but do your best to put yourself in their paws and imagine your home from their perspective. Electrical cords? Those look good to chew on! Human medications? Looks like a snack to me! Household chemicals? Aren't you curious what those taste like? Uncovered HVAC vents? Looks like an adventure awaits inside!
There are also plenty of plants that are toxic to cats. Although the following list is not comprehensive, here are some of the most common offenders: caladium, dumb cane, English ivy, lilies, mistletoe, oleander, and philodendron.
News Flash: Cats are climbers!
Imagine them climbing on everything around the house. Removing anything dangerous is great, but you also need to make sure you provide alternatives. Reserve some platforms, shelves, or cat trees for strategic locations/vantage points for your kitty to monitor their domain. One of the best is a window-mounted kitty seat as the outdoors entertains them immensely.
New kittens might be confident enough, but adult cats often need time to grow accustomed to all the new huge humans, strange sounds and smells that make up their new universe. Expect your new cat to find their own safe space in your house and try to respect that space. If you have multiple cats or pets, watch out for hot spots which are heavily contested spaces in the house. If possible, place a climbing tower in place of the hot spot, with multiple ways to enter/exit and avoid unfriendly encounters.
Sofa scratching is a common problem. Your cat does this so they can own the space alongside you and share the smells. No matter the sweet intention, you still don't need your favorite couch destroyed. Try a scratching post close to the problem area and gently redirect your cat there, and they will likely clue into it after a few redirections if they like the scratching post. There are many products and you may have to try out a couple before you find the one your cat can't resist.
Remain cognizant that your cat may need a little time to settle into its new environment. Let them come to you, as opposed to reaching out to pet them. This can be difficult if they are especially adorable, but letting them make the first moves ensures they are comfortable with their new space.
And finally, take your time to introduce new treats, catnip, and toys. Cats can be picky. But keep trying and they will find their groove.