I've found this:
https://shedsbylandserv.com/amish-built-animal-structures/chicken-coops/
I'm thinking that I'd go with one of the saltbox style ones, and build a run. I'll probably pitch it to my parents as 'If you're ready to spend this much money why not get much more for your money?"
Be sure to check the size--you don't want something else that's too small! Plan for 4 square feet of floor space per chicken, for both the current chickens and the others you hope to eventually have. So for 8 chickens (future number), you would want at least 32 square feet. That's 4 x 8, or 6x6 works too, or 5 x7. But look for a coop that claims to be one foot bigger in one direction, because so many coops have the nestboxes sticking out. Nestboxes do not count as floor space for the chickens.
And you may want to consider options that already have a run. Because if your parents ARE willing to buy something that is right, it WILL be easier for you than building it yourself.
Big projects take lots of time to build (just look at all the threads about people's coop builds, where they go on for months before getting done.) First you're going to be away at camp, and then school will start again fairly soon after that. So there will be limits on how much time you are able to spend building things.
Also, building things can take a certain amount of strength and size. I remember my Dad having a bunch of his co-workers come help put up the walls of a building. It wasn't that big, but it took a surprising number of strong adults to stand each wall up and connect them together.
Building something well also requires a certain amount of skill, and you've said you have no experience building things yet. Even as an adult, the things I build are often a bit crooked and wobbly--so what you build just may not work right the first time.
Because you cannot drive to buy materials for yourself, your parents would have to be involved at least that much. So no matter how much you assure them that you will do it all yourself, they will know that you cannot really do ALL of it.
And there's the question of using power tools. They can be dangerous, and they are expensive to buy if you don't already have them, but cutting everything with a hand saw makes the project take a LOT longer!
I'm not trying to say you "should not" build something, just suggesting that you consider carefully before committing to it. Especially because it looks like your parents are more inclined to buy something than to have you build it.