First of all: Thanks so much for adopting a rescue dog! Where other dog owners have been irresponsible not to alter their dog, you kindly jumped in to help out. Much appreciated.
Now, your rescue dog almost certainly is already altered: If the dog wasn't altered before ending up in the shelter, the shelter staff will have taken care of that. In addition, every shelter pays a vet to check the dog's health. Subject to what country you are in, they will also have microchipped the dog. That's already THREE worries taken off you!
Once you adopt the dog, you have the unique chance to welcome the dog into your family in a way that makes the rescue dog feel rescued, not relocated. You will notice that initially a rescue dog is in many ways like a puppy, because all is new to the dog, in your family and in your neighborhood. Indeed, best would be that you apply some fundamental puppy knowledge for the first four to six weeks: Socializing the rescue dog, fully house-training the dog, and training relaxed leash walks and off-leash walks.
But before we delve deeper into that, let's continue logically with our "decision tree": What brought you here?