Well, the best way, is if you can reuse something you already have...... such as dog run and dog house. Then you can tell your parents, it won't such a big investment. You can buy a roll of chicken wire, and cover the lower edge of the run, to keep chicks in. and the outside ground to keep predators from digging in. Over the top, to keep predators from flying in. Put the dog house up on a platform, add some ventilation, add a roost and some nests and your are in business. DO NOT BUY those cutesy chicken coops sold in stores. I do not think they are sturdy enough, have enough ventilation, or space.
Think of it as pets with benefits. Everyone loves fresh eggs. It is a fun hobby, you can join 4-H and show, or the local poultry club and show. It can be a life time hobby.
I would recommend starting with 3 hens, unless you have a larger family than 4-5 people. Eggs add up quick. Small flocks cost less in feed. Go out to your yard and decide where you could put a coop/run. Measure off the area. If you don't have enough space, pick a different hobby as not enough space is the cause for most of the problems with chickens.
Now if your family likes a garden, sell the idea of how rich chicken manure is...... but know that you will need a compost area because you must age the manure before you apply it. I have seen really nice layouts, where the chicken house is set up, so that durning the winter you turn into the garden area, so the birds do the clean up for you. Drastically reduces insects in the garden.
Tell your folks, that when you get extra eggs, you can give them to co workers or neighbors as a treat. I do that often, if someone does me a favor at work, I will send them a dozen or half a dozen of fresh eggs. People love it.
Tell them as a middle school/high school teacher, I know that students with a productive hobby, (rather than a non-productive hobby such as video games) are healthier both physically and mentally. They can meet people with similar interests.
Good Luck
Mrs K