I agree to go to your shelter and find a dog that has the perfect personality there.

There are lots of breeds that match your description. The ones that come to my mind are labrador retrievers and golden retrievers, because they are calm indoors but love to go jogging. Plus they are usually good with small animals, like a bird or cat. However, their puppy years aren't necessarily the most calm. That's why shelters are great; they have adult dogs too! Retrievers usually calm down around 2 years.

Breeds you have to be careful with are most of the spitz breeds --- they generally have very high prey drives and might take after your bird or kitty. Herding breeds can be great with small animals if they are raised with them. However, getting one that is unsocialized with small animals might not be the best idea --- herding is a moderated prey drive.

Good luck in finding your doggy! Being me, I would recommend the German shepherd dog and Catahoula leopard dog --- but they don't match your description.