Bunnies must be fixed. With bucks, it stops the unsociable behavior - eg spraying and aggression. With does, it eliminates the risk of uterine cancer. A very high proportion of unfixed female rabbits die of cancer at a young age. Having said that, I pay around $50 to get bunnies fixed - there are low cost clinics in many cities that charge far less than a vet.
Re vet bills, you can avoid these if you know how to care for a bunny properly. Rabbits are sensitive creatures, and if you don't treat them right, they get sick and die very easily. Proper habitat and feeding is essential. Our rabbits are on a very strict food regime: small amount of quality pellets in the morning - the same brand without fail, no cheap pet store brands. Unlimited Timothy hay, day and night. A selection of correct veggies in the evening - at least three per day, organic if possible, if not, fresh and well washed. (We grow a lot of our veggies for the rabbits during the summer, which is fun for the kids, saves $$s, and very educational).
If you keep your rabbit outside, don't expect a long life. RAbbits are extremely heat sensitive and can die at the drop of a hat if they get over heated. They are also prey animals, so if they are outside, you could well find them dead in the morning after a predator came to sniff around the cage.
If you keep it in a wire bottomed cage and leave it alone for hours, don't expect it to be friendly and be a healthy, good pet for your child. For the best pets, keep them inside, and allow them out for exercise regularly. Our rabbits live in large exercise pens and the kids go in and play with them for several hours a day. They also get variety - they come to different parts of the house most days, and go in an exercise pen in the garden UNDER STRICT SUPERVISION on cool days.
Once you get the hang of rabbit care, it is easy and can be trouble free. Any sign of not eating or ill health, and you have to get to the vet pronto. Any delay usually results in a dead rabbit. We spent about $500 on a rabbit that got sick, before we learned all we know now about rabbit care. The rabbit still died. Now, we rarely go to the vet, and I can trouble-shoot most problems myself. Proper routine and feeding eliminates the most common cause of sickness, which is digestion problems.
Rabbits are great pets, but you can't put them in a cage and throw them some food once a day. They are as much as a commitment as a dog, and I think, more than a cat. Having said that, they are also wonderful pets. Ours are all real members of the family, and we adore them. They each have a very distinct personality, and give the kids a lot of joy. In fact, just yesterday my kids took two of our rabbits to a rabbit show where they showed them, then entered them in showmanship competitions, and even a costume contest. The kids spent hours making costumes -one bunny was dressed as a lion, the other as a bumble bee. They were so cute, sitting all dressed up and posed for the judges until they got their ribbons. They honestly thrive on attention, so if your kid is likely to lose interest, don't get a rabbit. They have as much personality as a dog, and they deserve great homes where they are given attention and appreciated.
Finally, there are thousands of rabbits in shelters needing homes. Please adopt one, don't buy one off an irresponsible breeder. That way you usually get them fixed, and they have had health checks. One of our best rabbits came from the humane society, and is a total superstar. He runs to the gate to greet you whenever you walk through the door, and will snuggle for hours with the kids.
Good link for rabbit info and care: http://rabbit.org/