Would this be a good idea, or a bad one? (its long. And help from previous Pit Bull owners aprreciated)?

SO, I've been researching dogs for a while now. Mainly the large breeds and breeds I think I might like to have in the future. I have also been looking for a rescue puppy who needs a home. Now, in the household I live in, there are two parents, and to children, ages 12(girl) and 9(boy)(turning 10 in May). Age... show more SO, I've been researching dogs for a while now. Mainly the large breeds and breeds I think I might like to have in the future. I have also been looking for a rescue puppy who needs a home. Now, in the household I live in, there are two parents, and to children, ages 12(girl) and 9(boy)(turning 10 in May). Age 12, we'll call her...Cat. (she reminds everyone of a cat!) Shes great with all animals and shes never shown the slightest bit of fear to a dog. We own a dog currently, and she'll get down on the floor and wrestle with her. Now our current dog, is an Irish Wheaten Terrier, so shes not too big. (shes about four or five) Now, back in December, She got a puppy for Christmas. It was a Vizsla. We were told he was 10 weeks, but when we went to pick him up, the people said they made a mistake and he was actually 10 months. Being 10 months, he was already quite large and had some bad habits that were tough to break (separation anxiety) before school started again for Cat and, we'll call him Mouse. Mouse was deathly afraid of our new dog, and wanted nothing to do with him. Hes more of a cat person, and it took a while to warm up to the dog we have now. However he loves animals as well, but has a fear of them. He loves to help them and would take a rescue dog even if he didn't like it, as long as he knows hes helping it. We ended having to give away this dog, but are looking for a puppy as stated earlier. (we still have the Wheaten, but not the Vizsla)
Heres the question.
I found a rescue puppy, or should I say puppies, on the internet. Everyone all know that these types of dogs are dangerous, but if trained correctly, can be a great family pet that gets along with everyone. I guess I should get to the point now though. The mom is an American Pit Bull Terrier. The puppies are a mix, but the border doesn't know who or what the dad is. So I'm saying would it be a good idea to adopt one of these puppies from unknown lineage? I know especially with this breed, even the mixes, should have an extra careful search. On the add it says the border is full and finds dogs weekly. It also says the mom will nedd a home after the puppies are weaned, and puppies need homes fast.
I'm a little worried because we have a number of other pets: two cats, one who is only inside at night, we let her run around the front yard, she comes back at around the same time everyday, and the other lays around upstairs all day. No other pet is allowed up there. We also have birds, one is a miracle bird, its 21 years old and dies and relives everyday its crazy. We have fish, but not sure if thats a big difference. Not knowing what kind of history these puppies come from worries me a little bit. Would it be a smart idea to adopt one and give it a good home? Will it get along with our other pets?
Also if you think we should would it be a dog that
-Doesn't need to be taken on long walks every day
-Gets along with other pets
-Doesn't need a lot of grooming
-Can be trusted alone outside with our other dog for a few hours a day

I know Pit Bulls haven't the best reputation but I wouldn't mind giving one a chance. Also, if you think that its not a good idea to adopt one of these after they're old enough, theres four shepherd boxer mixes that I would like to adopt as well. Wichever one would be best can you please tell your opinion and reason(s). I think the Pit Bulls need a home more, but I want to do whats best for everyone.
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