People often compose photos so that the subject's face is in the center. However, it's actually better to have the whole body of the subject in the photo than have it be cut off. Even if their face is in a corner of the photo, they'll still be cute nonetheless. This also prevents unnecessary objects from getting into the photo, giving you a clean shot.
For cameras with a zoom function, operating the zoom lever activates the telephoto lens and enables taking a photo with the subject enlarged. Cats are cautious animals, so it's probably better to use a telephoto lens instead of trying to get close. If you use zoom, not only will you be able to get close to the subject (take an enlarged photo), you'll also be able to arrange the background.