When I was a kid we moved into a rented house. It had a mouse/rat problem. My mother put down rat poison. It got rid of the rats fine. Howesver, it stank of rotting rats for weeks. Since then I have never used rat poison.
Cats are a good idea but that will lead to a cat problem down the road. Probably rabies too. This reminds me of the children’s story about the king that had a mouse so he got a cat, then a dog.... and so on.
Howesver = However