A mouse can get a little bit bigger might be seen in the store, depends on the age of the mice being shown. A mouse typically shouldn't get too big.
Honestly, depends on the type of pets you have. I would not risk having a cat around them, just for the mere fact that a mouse cage tends to be smaller and easy to knock over. My rat cage was too heavy to be knocked over by a cat. Dogs can go either way with rodents depending on breed and temperament. This would not apply if you live in a place that does not allow cats or dogs, which I think you mentioned you did.