Consider how to limit access through-out your entire home until your pet is comfortable. Do you have baby-gates? Can you close doors?
Purchase food, toys, collars, litter, and supplies just before the animal arrives home.
Pick up anything that is tempting to eat or destroy. Prevention may solve headaches later. It is better to be safe and remove the item until you are sure it won’t be an issue. For example, move plants off the floor. Or, pick up your slippers.
Have “oops, I made a mistake” supplies on hand, in case of an accident – soap, water, paper towels, Nature’s Miracle, etc.
Plan on being there for the animal. Don’t rush out and leave the pet alone. Cats may need some quiet time to be alone to explore the house while dogs may need you around to monitor their activities.
Plan on getting a new collar and ID as soon as possible.
Research and select a vet before you pick up your new adopted friend.