we lost our last dog Ben in june he was a rescue dog and he was 18 years old he never really took much notice of the cats and vice versa but they just got on together .. Our new rescue dog we think is Doberman and german sheperd cross andd is a very bouncy dog due to only being a puppy.
Cats see territory in verticle spaces, not horizonal like dogs do...so they enjoy sitting up high and "staring down" on the inferior dogs lol It also makes them feel safer when the new scary dog is around just in case they try to sneak through the room and get spotted by the pup.
I personally have this one
its was $40 at walmart...as the other cat trees are ussually $150 and up. It goes floor to ceiling ( ten feet) and for $40 iam very impressed with it.
I would see if the cat likes dogs.. if he doesn't its worse than a dog not liking cats since cats can also hurt a dog pretty bad if it goes wrong. I would definitely introduced them somewhere they are not familiar with.