Getting a cat or kitten from a rescue group will be far better way to go. You can ask a rescue group for a dog friendly cat. The cats in our rescue group are rated for multiple cat household, children, dogs, indoor/outdoor. The foster person should answer your question regarding hyper dogs and the cat they are fostering.

Get a tall scratching post. Atleast 3 feet in height so the cat can stand up on his hind leg stretch out and reach with front legs to scratch. Also having several cheap corrugated cardboard scratching post works wonder.

Litterbox clean every day! We also put some Litterbox treatment from Nature's Miracle to deal with the smell.

And what most everyone else said. We don't like cats to go outside. They get hit by a car, pick up FeLV/FIV when they get bit, come home all chewed up after a cat fight, rabies, coyote, barn owl...