Shopping in Edinburgh

Hello! I’m an international student joining my course at the University of Edinburgh this coming week. I am from a tropical country so when it comes to warm clothes I haven’t packed anything from home except for some thermal inner wear and lightweight knitwear. I plan on buying essentials such as trench coats, rain macs etc. from Edinburgh itself. Could anyone recommend good stores close to Leith Walk for shopping? Preferably thrift/ charity shops since I am on a budget. Thanks!