DO NOT LISTEN TO THESE PEOPLE! The only thing these people are suggesting is the crap they hear from some untrue bull**** stories. Do not get a Pit Bull, Rottweiler, Mastiff, Boxer, German Shepard, etc..
Note that you are making a commitment for at least 10-15 years! Do not just get a dog to chase some damn cats and then forget about it, it is a huge responsibility. These people have listed dogs that are proven working dogs and have their needs. All of those dogs needs way more then an hour of exercise a day to be happy, note the time you have to spend with them, the food and treats, the vet bills, and amongst other expenses.
Please do not listen to these people. If you still want a dog, what kind of experience with dogs do you have? Just about any dog will manage to get rid of your cat problem in the yard, and note most small game hunting dogs are tiny (ex: Jack Russell Terrier).
Note this is my hobby, I spend a great deal of time on thiss. I am currently working as a vet assistant and on my yearly vications am into working dog events (French Ring and Schutzhund). I absolutely hate people who go around doing irresponsible bull**** like this.
That is besides the point that your dog can get hurt amongst other things lose an eye or two. Look into some cat poison or repellents...