You should try to stick with your dog's current diet if at all possible. He doesn't need stomach trouble or loose stools right now. He can be weaned off of the old diet slowly.
If you can, bring your dog's old bedding, towel, or favourite toy from his prior home. He can feel at ease if he's feeling "homesick" because even after washing, a trace of the aroma of his favourite locations and people will remain.
Limit your dog's house access initially. He may have lived mostly in a run or container. He may feel overwhelmed or regress in his housetraining in a larger setting. Keep him leashed or in a nearby ex-pen. Leave the house with a container or ex-pen.
Maintain a regimen with regular meals, walks, etc. Your dog will be less agitated if you stick to his routine. As he becomes used to your home, you can change the routine.
It's natural to want to shower your new puppy with affection, but remember that giving him too many treats can cause him discomfort in the digestive tract. Give him some non-destructive chew toys to play with so he doesn't become bored and start gnawing on your furniture.
Safeguard your new family member. Even in a fenced yard, he should initially be leashed. He doesn't know where "home" is, and you don't know how well he jumps or digs. If he isn't already, microchip and tag your dog. Your phone number can be embroidered or embossed on a collar.
Take the new addition to the family on regular walks. Don't venture outside of leashed walks and fenced-in games of fetch. In the winter, little dogs can play fetch down a carpeted hallway. You want your dog to be secure while he releases his anxious energy via play.
Discuss family norms. Consistency. Unfair if one person lets your dog on the sofa while another doesn't. Cuddles and corrections will confuse and upset him. He prefers uniform command words. Call your dog "come" or "here". Pick. No nicknames or complicated terms yet.
Dogs "carry" This baggage can be "good," like learning obedience commands and tricks, or "evil," like being comfortable knocking over trash cans or stealing food. Eliminating bad habits takes time. Ecology first. Dogs can't surf clean counters. Hide trash. Simplify everyone's life now. Don't clean your first week.