Have treats for the cat ready to go. A perceived loss of attention can cause negative behaviors but having something to balance that loss can help to smooth the transition.
Dogs thrive on consistency, so be sure to bring home as many of his toys, blankets, and treats as you can, and keep the food consistent. Keep feeding schedules, walking schedules, and bedtimes as “normal” as you can. These things can help to keep the stress of rehoming low, though the 3-3-3 rule posted by another commenter is likely to be close to your experience.
If his humans have done training, get a list of the cues he knows. If they can shoot a quick video of how they give the cues, that can help bridge the communication gap between you and the pup more quickly - dogs are mostly visual animals, so body position and any hand signals are a large part of how the dog knows what’s being asked of him.
Have a place for the cat to get away from the dog, and do introductions slowly. Have a place for the dog to get away from the cat, as well. Supervise interactions and play, and be ready to intervene/distract until you’re confident that they’re each respecting each other’s play intensity. If one animal is looking to stop playing, help the other learn to respect that with praise, treats, or physical affection. In that vein - every mammal on earth uses laughing to communicate play intentions. Rapid sneezing is dog laughter. Some dogs are verbal during play - barking and growling is a normal play occurrence and you should be looking at body language in addition to listening.
Dogs are bad at generalizing. Just because he’s been potty trained does not mean he’ll know where he’s supposed to do his business at your home. This used to be one of the biggest learning curves I’d have to help clients through, so consider him to just not be housetrained. Have some enzymatic cleaner on hand for cleanup, to prevent reoccurrence of accidents in your home. Puppy pads are most useful for cleaning after the fact - putting them down during housetraining can be confusing for dogs, and I don’t recommend them.
Leslie McDevitt, Sophia Yin, and Karen Pryor are my top three recommended authors for learning to communicate effectively with dogs. If you’re looking for video lessons, Kikopup (Emily Larlham) is one of the best around.
If you have other questions I’m happy to answer them to the best of my ability.