I used to have a cat that would kill mice she was very proud of it too. She liked dogs too if you have a sociable dog a kitten will learn to blend in. My cat killed mice on her own with no training some cats just have that instinct some don't though. She killed mice outside and brought them in to me haha. One mice made the mistake of trying to build a nest in my house, she waited outside his hole for hours and got him as soon as he came out. A snake would also kill but they are not fast, even if you put a mouse in it's cage confined the snake just sits there sometimes for hours until he kills it. A cat is the best type it should be a tom cat or a small type of cat they seem to have more instinct then the fat or fluffy fur cats.