I've only been out to my parents for about 7-8 weeks, and I'll be a minor for a few years yet. For most of my teenage life, I'v worn a zip-up hoodie every day, even in the summer (except for this year -our summers usually get up to 105 F, this year it was 117 F). I actually had a friend of mine get me a binder for my birthday one year. She ordered it and had it shipped to her house, then slipped it into my backpack the next school day. I was parnoid about my parents noticing, but the hoodie also helped hide that they were flatter than usual.
I found that zip-up hoodies are better at hiding the lumps than pullover ones. Also, I would wear a sports bra that's one size smaller than what I'd need. I couldn't go with no kind of bra, because then the stuff would move around and make themselves obvious. A regular bra, even those with no wire or padding, wouldn't hide them. I can't give any tips to large-chested individuals, though, because I'm a size 32B, but I'm only a B because the lumps are wide - if it weren't for that, I'd be an A because they're kind of flattened, which is partially due to only ever wearing somewhat tight sportsbras.
I never had any luck with button-up shirts because my mother would go on a rampage to make sure that said shirts didn't make me look like a boy. I found that general t-shirts were the best, preferably one size too big. The Fossil brand men's shirts were the best. They're the somewhat unisex-type men's shirts, so they didn't raise any suspicion and they have clever designs on them (at least, I think they do!). One of the shirts I got from there, I could pass in when even wearing a regular bra!

So, I hope that helps somewhat. Sorry, I'm not very good at giving tips.