While rescuing a dog from a shelter is a noble cause, your reason above is exactly why I won't do it...If it were just me, I would have no problem taking in a full grown alpha male, but I have a 4 year old son and I have no idea what a stray dog is capable of...If I train it from a puppy, I know exactly what he/she is capable of.
BTW, pits are fantastic dogs...The few pits I know all have competent owners and they are among the sweetest dogs I have ever encountered.
Puppies come through the shelter all the time, but you may have to be patient to get a breed/mix you are looking for because they go a lot faster than older dogs.