Second hand dogs can come from many places, shelters, rescues, someone who just can't or doesn't want to keep their dog anymore and they can be any breed or mix. Adding a second hand dog to your life is truly a great thing for both the dog and yourself. Some dogs have literally been saved from death and some from a long and stressful life in a cage. Many of these dogs have behavior issues that the first guardians did not want to deal with, some have none and the sheer fact that they were a dog is what caused them to be in this situation.
No matter who the dog is or where she comes from there are things you need to be aware of when looking for a second hand dog. First is temperament, I am very cautious about bringing home adult dogs with children when the dogs background is not known. The utmost of care must be taken when choosing a dog to bring into a family with small children. Some rescues and shelters do temperament testing and some do none at all. You want to stay away from the ones that don't temperament test. I know of at least a few that don't test and there have been people and children hurt because of it.
There are alot of great dogs that end up in shelters but there are also some not so great dogs there. Honestly there are so many wonderful dogs who are homeless that it is worth the time and effort to find your wonderful dog there. If you are looking for a particular breed then you are going to have a much better chance at a rescue. Many rescues are fostered in someones home which is great because this gives the foster person a chance to see what the dog is really like. And they will be able to enlighten you on some of the behavior issues they have seen.
A shelter is a very stressful place for a dog so often you won't know what the dog you are bringing home is truly like for several months. I have had many clients say that their shelter dog changed so much over the past months they had been with them. A shelter dog is in a state of limbo, they don't know where they are or why they are there. When you bring them home it is the same thing but less stressful. As they start to realize that this is their new home they start to relax and the real dog begins to emerge.
When you go and start to look just like going to a breeder, don't make any impulse decisions. I also know many people who have brought home second hand dogs only to realize this is not the dog they should have brought home. If it is a mix you are looking at what is the best guess of what's in that mix? This can really help with behavior you may need to deal with down the road. But, if there is just no guessing on what type of mix this may be then you have to go strictly on the now temperament.
My biggest advice is go somewhere where they temperament test. It is not a guarantee but this means that the shelter or rescue are concerned that the dog is not going to need to be rehomed again, that is huge. You do not want a place to hand you a leash the minute you walk in just to place dogs, this is just a never ended vicious circle.