Should I ask my landlord (who I have a good relationship with and a really good deal on rent), just get one of the cats without telling her, or not get one? If I should get one, which one?
You said you have a good relationship with them, I say to give it a try and ask and if they say no eat the bullet and don't get the cat. If you get one and they then know about it, it can ruin both relationship and rent deal
That's my thoughts on your question
As of which one... This one is hard, the right one?