If you have chosen a dog from a rescue shelter, extra care should be taken when bringing your pet into your home.
Make sure that your new dog has an area where he can go which will keep him safe and also keep your home safe from a curious new dog. A crate can be one of the easiest ways to make such an area for your dog. A rescue dog is likely to have spent a lot of their time in a small run, so they will feel at home and safe in a crate. This gives them a comfortable place to go when they are feeling overwhelmed in new surroundings.
Although your rescue dog is unlikely to be a puppy, you should treat him as such for the first few weeks in your home. You will have no knowledge of how your new dog is likely to behave in his surroundings, so you need to assume that he can get up to the same kind of mischief as a little puppy when exploring your home.
You will need to encourage potty training and are likely to spend time training your dog in obedience. Going to classes will help you train your new dog and also let you see how he behaves around other animals. Although a responsible shelter will probably provide you with assurances on the health of your new dog, you should also take him to the vets to ensure that they have a thorough check up for additional peace of mind.