I agree with some sort of terrier dog... I have two pit bulls

ey both chase deer (I don't let them chase them farther than the edge of the yard)
:very short hair and don't smell like icky dog (I bathe them once in spring, once in fall and anytime they roll in something
really gross)

ey are very smart and excelled at agility classes and love having their minds challenged.
:very attached to their people

urs live here happily with our house cat (although they grew up with this cat and I wouldn't necessarily trust them around
EVERY cat)
:Carrie loves to catch mice, bats, small birds, squirrels and especially loves digging up moles in the yard. She has caught one of our chickens before, but when hollered at dropped it without puncturing skin. Marley just likes to chase things that move, but he has never killed anything.
They do need a lot of exercise and mental stimulation (at least ours do) or they get bored and start destroying stuff in the house, but I think a terrier is just what you would be looking for.