start small, small number of hens, I had 5 all winter, kept my family of three in eggs, plus plenty to give away. Get a sturdy breed, like red stars, barred rocks, or RIR or buff orpingtons. They are good layers and good hens.
A small coop does not cost a fortune, a small run is cheaper. Start small, the mess is smaller, and the feed bill is smaller. Feed all scraps, and when you clean the fridge, all of that too. I have seen people post that they only feed what they would eat, but let me tell you a chicken is not that picky.
You do need understand and be able to explain to your kids about death. It does happen, it is a fact of life, and I think it is a good lesson for children to learn, culling animals may have to be done. Some here give them away, but lot's of people process them for food. It is a good fact of life to teach children too.
It can be done expensively or economically, like anything else. Start up costs can get out of hand, but stop and think how they did it 100 years ago, and they had successful flocks. It always keeps me reasonable.
Also, I agree with an above post, no veterinary bills, it is a chicken.
Mrs.K