I'm thinking of buying a rabbit. Can anyone help with advice?

My daughter is 4.5 yrs old and my son is nearly 3 yrs old and I'm thinking of buying them a rabbit. I have never had a rabbit before nor have I ever known anyone to have one. I want to find out a few things. Are they a non expensive pet to have, do they require vet attention for vaccinations or anything else, what do they eat, do they bite people and are they good with young children. Also if we do get one, it will be sleeping under our huge verandah in it's cage and we sometimes get neighbourhood cats running through our back yard and was wondering will a cat try and kill the rabbit or will the rabbit be safe. Is a male rabbit better than a female rabbit or vise-vera and how long do they live for and what breed of rabbit do you think will best suit us? Oh, I have heard of drawf rabbits, what are they like? Thanks