I was forced into showing rabbits because my aunt raised them for fun. I showed for 10 years including the state fair. Needless to say those trophys are in a closet while the cattle and pig trophys are still out.
Call your extension office and ask who the rabbit superintendant is, then talk to them, they will get you in touch with whoever raises rabbits in the area.
Easiest way in my opinion is with meat rabbits, such as californians. Really all you have to worry about is keeping them alive. Just buy rabbit food at your local farm store. Make sure they dont freeze to death or die of heat. Make sure your dogs dont kill them. Make sure that whatever you use as a hutch is not rusty or it will discolor the fur and that is frowned upon. Make your kids hold them so they dont flip out when you have to show them. Prepare your kids to have life long scars on their arms from those little devil spawns.
DO NOT BUY BREEDING RABBITS: Breeding rabbits is stupid and should only be done buy stupid "rabbit" people. Just buy new ones each year and sell the others at the livestock sale. The last thing you want to deal with is keeping rabbits over the winter. If your kid argues, lie to them and tell them thats the rules. Dont listen to people that try to sell you some "awesome pedigree" rabbit, its a rabbit. Not a show steer. Who the hell cares.
Do not let the rabbits in your house, treat them as livestock obviously. While the project is stupid and somewhat embarassing it did actually teach me to do chores and crap before I was able to show real animals at state and county fair.
If you tell me where you are located I can possibly hook you up. Southwest IA?