I have one cat, and she's been absolutely no problem.
I had a bunch of people freaking out at me to get rid of her, because she would suffocate my child, steal her breath by licking the milk on her lips, etc... And .Asia couldn't care less about the baby. When she's cold, she curls up between my ankles. She doesn't go near the baby.
And as far as the cat hair, if you maintain a fairly clean house already, it won't be a problem. Vaccuum your floors and couches at least once a week and you're cool.
Jealousy in dogs is a different issue though. You can google "dogs and babies" or something to that effect and there's tons of articles online that discuss it. I think it really depends on your dog's temperament.