If you have children and all your time is spent at soccer games and school activities, unless your Greyhound can be part of the activities, you don't have time for a dog. Dogs are social animals that need physical and mental stimulation. And just because they are quiet, gentle dogs, doesn't mean they don't need to be trained. Training isn't about obedience as much as it's about forming a trusting relationship and establishing a way to communicate. Dogs and children are not as compatible as Hollywood would have you believe.
Greyhounds have little padding and they have skin that tears easily.
They have little protection from falling toddlers or rowdy children. They have a quiet nature and do best in a tranquil environment. If any of your children are under school age or your kids are particularly active, don't get a Greyhound. I'd even go a step farther and tell you don't get any adult dog if you have young children. Dog bites are one of the leading causes of death in children.