It's hard to determine if you should get a bird with cats in the house. Some cats won't bother the bird, but if yours pick on the bird while it's in the cage you've got a bad match and you should not have birds. It just because it would be cruel and the bird would live in a state of torment.
In some cases, it's bad to allow your bird to fly- if it encourages the cats to attack by triggering predator instincts. In other cases it's fine, but you have to keep a good eye on your bird. Mine both like to eat wires and cables, but Potato will destroy my furniture and most anything in beak range if not watched.
You may have to keep your bird in a room where it can be secluded from the cats while noone is home, for safety.
Really, it all depends on your take on birds. I like mine to be able to fly, but it does deter the bonding with your bird. I recommend the Pionus species if you haven't picked yet. They make excellent pets and are generally very quiet.