TL;DR
Start small: one quiet room, a litter box they can see, food on a schedule, and a vet visit booked for day 3-5. Everything else can wait until week two.
Day one: one room, not the whole house
A new kitten in a new house is a small animal in a very big world. Pick one quiet room — a bedroom or office is perfect — and set it up before you bring them home. Litter box in one corner, food and water on the opposite wall, a soft bed, and a couple of toys.
Let them come out of the carrier on their own time. Sit on the floor, read a book, and wait. Most kittens are exploring the room within 20 minutes.
Food, water, and the litter box
Feed the same food they were eating before you brought them home for at least the first week — a diet change on top of a home change is one stressor too many. If you want to switch, do it slowly over 7-10 days after they've settled.
Kittens usually know how to use a litter box, but they need one they can climb into. A low-sided tray with a fine, unscented litter works for almost every kitten.
Book the vet visit for day 3-5
You want a wellness check within the first week — partly for peace of mind, partly to get on a vaccine and deworming schedule. Bring any paperwork from the breeder or shelter, and a fresh stool sample if you can.
Expanding the world
After 3-4 days in the starter room, open the door and let them explore on their terms. Don't move the litter box for another week — let them come back to it until they clearly know the layout of the house.