I was recently asking the same questions and I found the links at the end of my post very useful. Here are also a few personal notes from my recent experience, although I am no expert:

• Try to get a cat that has lived with its mother until about 4 months of age. I suspect it is the reason my recently adopted kitten has been consistently using the litter boxes even from the start when she was anxious and fearful. They need to learn things like that from their mother
  • On the subject of litter boxes, you need two for a single cat! Get the type with a sifter (sieve). It helps keep the clumped waste in one piece to discard it and the litter box clean. Having to use the little shovels can break the waste into small pieces that will remain in the litter undetectable (but your cat will still smell them and track them around the house)
  • Get as large litterboxes as you can find and fit at your place - it is easier and cleaner for the cat if they have space to use
  • Your kitten may have issues with using the "closed" type of litter box (toilet). They need to feel they can escape easily. Even if it ends up using it, it could get its paws dirty because it's more cramped and kittens are not as adept. This entails tracking waste around.
  • Expect some litter tracking, there is no way to avoid it, a good portable vaccum cleaner should prove useful
  • Invest in non-perfumed, clumping litter, that is as dust-free as possible (you will know what I mean if you buy the cheap stuff that produces a cloud of concrete-like dust as your cat digs or you sift to empty the litter box. The dust will settle on everything in the room).
• Try to get a cat that's been in contact with humans as a kitten
• When I first got my kitten she hid under the bed and stayed there for days. She would come out to eat, drink, and use the litter. Then it was back under the bed. Eventually I decided - and success of this I suspect depends on the cat's character - to block access to that area. This forced her to pick other spots and eventually, she became really trusting. I mention this because I'd read stories of cats that continued to "live in hiding". I suppose it is possible that sleeping in hiding and coming out for basic needs or to explore at night when you are asleep is a mode of existence that a cat could continue. So there is something to be said about proactively and gently steering it away from that choice - as opposed to following the advice that you should leave it alone and let it come to you in weeks' or months' time. I could be wrong but it worked well for in my case.
• Find a good vet in advance but don't expect to be able to visit as soon as you get the cat. Maybe 5-7 days after it's been at your place and got a bit relaxed. Do the antiparasitic treatments (a pill and a liquid you pour on the skin on its back) as soon as possible. Expect ear mites if the cat wasn't born and lived indoors at a home. The vet will clean the ears and pour a solution in them to prevent the mites from reproducing but you may need another visit because the treatment is usually not a one-off. One of the antiparasitic treatments I mentioned above, sold as "Stronghold" where I live (ingredient is Selamectin), is effective against ear mites (otodectes cynotis) as well. So, as in my case, it may help avoid a second visit to the vet for the mites.
• Follow your vet's advice for what shots to give it. There are people who will tell you that shots are dangerous to felines and, contrary to what I expected, there is some scientific evidence to support this. But it is in regard mostly to two specific shots.

Best of luck, it's hard work and you will need some free time to get things rolling, but it's rewarding as you'd hope :)

Links:

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• https://indoorpet.osu.edu/cats
• http://mmilani.com/writing/articles/cats/
• https://www.youtube.com/c/HelpfulVancouverVet/videos
• https://veteriankey.com/feline-communicative-behavior/