If you new cat is less than a year old, feed kitten formula food until it is, or start mixing cat formula with kitten formula food if it's almost a year. Read the ingredients list on the dry food bags. The first three ingredients will make up the bulk of the food. AT LEAST one of these should be a good meat source. If it says chicken or beef or fish or such, that means the human grade edible portions of the animal, and that's good. If it says (something) byproducts, that means the ground up organs not ususally eaten by humans, like lungs, stomach and such, and that's not what's meant by a "good" meat source. This is not neccessarly bad, but it's not as nutritious as meat. Corn is not digestable and is basicly filler, but it does count toward the minimum amount of protien required. If you can afford the the grain free cat food, that's best. If you have to go cheaper, remember what I said about the first three ingredients. There are some of the grocerystore brands that are adequate. But if all you see listed is byproducts, and you're going, "Where's the meat?" that food is garbage I wouldn't feed a feral. Ask where you get your cat from what they were feeding it. You might have to get a small bit of that (good or bad) to mix with whatever you're going to feed to prevent stomach upsets from a sudden change.
Get a basic litterbox big enough for an adult cat. Ask whar type of litter the shelter or whatever was using, clumping or non-clumping, and stick to that at first. Some catrs don't care what you use, but some can be fussy. Put the box in a quiet location, preferably where the cat won't be cornered by other animals or they might not use it. That's one reason some cat don't like covered boxes; no back door. In a single cat home that's not much of a problem, but if you have a dog it still might be.
Set up a room where that cat can be kept for the first few days while it gets used to the new home. Put the litter box and food and water in with the cat. Once it's comfortable with the room and with you, start letting it out to explore. If you plan to have the litter box in a different location, set a second box up there. When that cat is reliably using the second box too, you can remove the first one.
Get a good scratching post and have it available to the cat from day one. Play with it around the post, put treats on top, etc to encourage scratching on the post. If neccessary, cover the corners of upholstered furniture with double stick tape or foil to discourage stratching on these surfaces. Your new cat should soon decide that the post is nicer.