Getting a six month old puppy soon

Hello! I am getting a puppy next week. They think she’s six months old. I’m going to take her to the vet to find out for sure, but right now that’s what I have to go on. We have no idea what exactly she is, but she’s already got some adult teeth so we think she’s about done growing. They’re giving her to me because she’s terrified of their kids. Apparently she was terrified at the shelter too and just cowered in her pen. She’s been fixed, but they’ve been unable to train her in anyway due to her refusing to leave the kennel when the children are home. My question is how different is it to train a six month old puppy versus a younger puppy? Especially when they’re so afraid of things? Like what am I in for? Because I’ve only really trained puppies from a younger age. Also she’s going to be a small dog we think. Do they require different ways of training then big dogs? I’ve never had a small dog before. She’s sooo cute and I love her already, and I just want to do the best I possibly can for her.