Warn your dad, some of them will get sick and die, but it is nothing that you all can't handle. Just know, he is 100% right about that.
A lot of people regret getting a $200 pre-fab coop. They break down easily and usually aren't warm enough, (does it get really cold where you live?). You might want to look at craigslist to see if their is any other options. Or you can get the 200 one to hold you over and then start seeing if you can build or buy a better one.
Barred rocks are easy to sex, generally. Her legs should be black, and her feathering will be darker in general, you can look up pictures of barred rock sexing on here. Maybe you want to get all barred rocks if you can't have roosters where you live.
All these folks on here are just worried for the chick and for you. They know how much work, sweat, tears, time and money get poured into these darling little creatures. I think it is great that you are deciding to do something to bring more meaning to your life, and teach you about animal husbandry. Teenagers need that stuff so bad. Just know, all these folks are for you, not against you, they were just concerned.