These are two common misconceptions about spaying. You will do so much more for the health of your pet by spaying before the first heat. It has been reported that by doing so, you will reduce the chance of mammary (breast) cancer in your pet by as much as 97% over their lifetime.
The chance of other reproductive cancers (uterine, ovarian, mammary) and uterine infection is eliminated in spayed animals. Even after the first heat, spaying will reduce the risks of certain cancers and eliminate reproductive organ disease.
Providing a loving environment for your pet, proper health care, and proper training will be the most influential benefit to maintaining a happy pet that fits into your family.