First of all, make sure your new pup is tired out when you start to train. Give her a long romp or walks and games of fetch. That way she'll have less energy to be crazy when training. But yes, the "your choice" game is a very good idea.
In terms of the other dog, it's not about dominance or "being friendly", so much as the adult dog likely trying to teach your puppy manners, or telling her to go away. Just like people, some dogs don't like kids! Sometimes it's really good for a puppy to get disciplined by a stable adult but since I don't know this dog I would be cautious and monitor their interactions. Just don't scold the adult dog for growling or snapping.
In terms of the other dog, it's not about dominance or "being friendly", so much as the adult dog likely trying to teach your puppy manners, or telling her to go away. Just like people, some dogs don't like kids! Sometimes it's really good for a puppy to get disciplined by a stable adult but since I don't know this dog I would be cautious and monitor their interactions. Just don't scold the adult dog for growling or snapping.