Try to get a cat that doesn't shed too much and/or has lots of dander. We have two cats. One is a small short-hair, very dainty, who barely sheds and has no dander. The other is a stockier cat with a double-thick short-hair coat that sheds year-round and has lots of dander. The latter is a lap cat, but her dander gives everyone problems, and petting her can mean a cloud of loose hairs in the air (even with daily brushing).