The peacoat is not cool, forget it.
The second one - if it is also designed for school you may need to read the uniform rules. Some have quite strict requirements. Also, if she wears a blazer it needs to fit underneath and I found belted coats are quite narrow.
DD wears mainly tresspass coats, one reason is that they are more waterproof than your average puff-style coat. She also has a coat matching the school's rule which are very different and it means they don't fit any outdoor activity so pointless for being outside, or in her case, being on trips with the scouts.