The trouble is there are no hard and fast rules about what combinations will, and won't, work and sometimes it's just a matter of try it and see.
For example we have the Lurcher and we used to have 2 cats. Some lurchers and greyhounds get on fine with cats, others can't live in a house with them, or any small furry animals, because of their excessive prey drive. We got our lurcher as a puppy, and she was brought up around a number of different animals, so the chances were good that she would learn not to chase our cats.
Unfortunately we had not reckoned with the temperament of our cats. Our cats have lived with the Old Boy, our 9 year old collie cross, for years, without any inter species friction. But along came the puppy, who yapped a bit, the cats took off, the puppy chased them, and so a habit was born.
If even one of our cats had been a bit tougher, and given the Lurcher a sharp whack across the nose for being so nosey or just stayed sleeping, rather than fleeing the room I'm sure things would have been different.
But now we have two cats who refuse to enter the house but deign to enter our separate utility room now and again. We leave food out for them and replace it when necessary, but they are obviously eating elsewhere as 7.5 kgs of dried food has now lasted us almost a year!
And I can now tell you exactly how embarrassing it is to have a neighbour from across-the-way and down-a-bit come over to you and ask if you can scan the 'stray' cat that's been hanging around their house for the last few months, for a microchip.Of course, I didn't need to scan it; when she described the big ginger tom that was camping out at theirs, I knew it was one of ours.
You can't tell a cat where to live, so while she doesn't want to adopt Ginger, she's agreed to feed him for us and will notify me if he needs any veterinary attention.
We don't know where our other cat is eating, but it's obviously somewhere with generous proportions as he's looking a lot rounder than he used to. He is long haired and really needs regular grooming, but obviously isn't getting this atm so needs to have his knots shaved. I'm going to have to wait until I find him in the utility room to have a go at sedating him so I can give him a good grooming.
On the other hand, we have rats, and used to have guinea pigs, that the Lurcher has showed no interest in at all. It's only cats she hates; this is something it would have been useful to know before we got her.
Cats are a common factor in many inter species problems as they can be both 'prey' and 'predator'.
Many a pet rodent, bird or fish has met it's end via the family cat. I've also been told a story about a family cat who ate 3 newborn chihuahua pups, when the owners were out at work. I'm inclined to believe it; puppies of that size would make a convenient meal for a cat bored with dried biscuits.
This doesn't mean you can't have a bird/rodent/fish if you have a cat, but be sensible. Don't let the prey species roam freely around a room/house with a cat in it. Not even if it's a geriatric cat with arthritis and kidney failure. Cats are killing machines and some will respond energetically to the presence of prey even while on deaths door.
Make sure the cage or tank you use to house your small pets is sturdy enough to keep the possible victim in, and the cat out. It's a case of you get what you pay for. Bars are better than plastic enclosures for small furries, but check the clips that hold bars to plastic trays are not going to give way to a determined cat. It's a good idea to keep the cage in a room that can be closed off from other pets when the house is empty of humans.
Our cats were regular hunters of mice and brought in the odd bird, but they were uninterested in both the rats and guinea pigs that shared our house with them.
It goes to show that you just can't tell.