Treats are a really helpful tool. Use treats to teach the cat where they *can* go, where they should scratch, what they should play with, to go in the crate, etc. Some cats even respond to command training! Finding treats your cat likes is super helpful, and there are a lot out there. Freeze-dried chicken is a favorite in our house, but so are special dental treats. I've seen treats made for calming cats, treats in all different flavors, you name it. Try things out.
Speaking of treats: be EXTREMELY wary about people food that you give your cat. The ASPCA has a really great, searchable list of plants that are toxic to cats (and dogs, and horses if you please) here: https://www.aspca.org/pet-care/animal-poison-control/toxic-and-non-toxic-plants
There are other foods they shouldn't have, but this covers a lot of herbs and plants, and flowers, that might be in your house or in your food. Good page to bookmark! Garlic and onion are obviously a no-go, but otherwise, table scraps are a good rare treat.
If you've ever seen "Jun's Kitchen" on Youtube, he has a really good relationship with his cats around cooking, and he's explained how he cooks with them. He lets them smell his ingredients because most of the time they're just curious, and it provides them with a little enrichment to smell new things. As long as you're careful, this is fun for everyone.
If your cat is shy, make sure they have places they can go that are quiet and undisturbed. If you don't create these places, they will make their own, and you won't like it. My cat found those places under my bed and inside a little covered cat bed. Allowing them to choose when they interact helps them warm up to you. Forced interaction always ends in tears for someone.
You've probably seen this one before, but please please please keep your cat indoors. The risks of having an outdoor cat are huge and expensive. That being said, a collar is still a good idea, because on the off chance they make a break for it, a collar with a name tag on it could help, and so could microchipping if you can manage it. Breakaway collars make sure your cat won't be choked if their collar gets caught. Also, if your cat has a tendency to hide, a bell might be a good idea - I use one to find out where my cat is, because she's very stealthy.
CATS CAN FIT INTO ANY SPACE THEIR HEAD FITS INTO. This is not always a good thing! Be mindful of this when cat-proofing.
If your scratching post/scratching furniture has strings coming off of it, sharp staples sticking out or anything else, it's a hazard. Loops of rope can choke a cat. Cut these, repair with your own rope/staples, or, if the furniture is unrecoverable, you might have to toss it. Keep an eye on that as your cat wears down the post/other.
Brushing your cat can decrease/prevent hairballs. Despite popular misconception, this isn't inherent to owning a cat. Some cats have it worse than others. I have a shorthair, for her it's not a problem at all, as long as I brush her every so often. Cats actually need to eat some of their own hair, for digestion reasons I won't get into here, if I recall? But too much isn't great. Regular brushing will be a lifesaver.
If your cat trusts you, you can file or clip their nails yourself. This is... Tricky, and something you'll have to figure out with your cat. Listen to them, work with them. I do my cat's nails a few claws at a time, depending on what she tolerates at the time, when she's chilled out and sleepy. If she pulls her paw away repeatedly, we call it a day. Some cats hate hate hate their paws being touched. Treat bribery might fix this, it might not. Depends on the cat. In a worst-case scenario, for nails OR medicine, blanket burritos are a great option, but you will not score any friendship points for them.
Hope this helps, good luck!
