Don't decide on a kitten that sounds like the best match for your family, without taking into consideration the often WIDE variation in physical and personality characteristics of individual kittens. Make sure to spend time and get to know the actual kitten you are going to adopt as much as possible, before deciding to adopt the individual kitten.
Don't adopt a new kitten without doing some self-reflection, planning, and research first. How much time do you have in your life right now to bring in a new kitten that may require training? Are you financially ready if your new kitten is injured, or gets sick?
Don't make an impulse decision on-site. It can be overwhelming at an adoption event when there are so many adorable furry faces begging you with their sad eyes to "pick me pick me" and take them home. I f you get emotional in an adoption setting, take a more objective family member or friend along to make sure you are making as good and rational a choice for your lifestyle and pet experience.
Don't let your kids sway you to pick an inappropriate kitten. While involving your children in the kitten adoption selection and adoption process is a wonderful way to teach them about responsible pet ownership and many other important life lessons, you as the adult need to make sure the kitten you adopt is a good selection. Do involve children in age-appropriate decision making parts of the adoption process: they can help pick out the new kitten's toys, or a collar, and certainly making sure they get along with with the kitten is important.