Don't get just one cat. Get more than one. Get several.
You're right - Cat 1 and Cat 2 will probably do nothing. Most people won't even think they exist. Cat 3 will do most of the work, but won't harrass rats beyond 100 meters. Cat 4 needs motivation - give it a small token, like a ring.
Cat 5 can be faster than Cat 3, but like Cat 3, speed and response begin to attenuate after 100 meters. They start dropping packets, which should promptly be buried in the litter box. In the event that rodents bite back, you should consider shielding Cat 5.
Cat 6 is extremely fast with very little latency, but inflexible and difficult to work with. I use them in my fruit pantry, where rats ate "twisted pears"