Ive never flown on a plane before

Taking a trip to CO here in a few months. We do not plan on purchasing luggage space (however you word it) and just going with carry on item. I understand thats one bag right? Do i get to bring my purse or solely the carry on bag? I also need to bring my winter coat but it will take up so much space in my bag. Whats the rules on that? What are newbie flight rules i need to know? Google is so overwhelming and theres so many websites to go off. I understand the shampoo and conditioner type stuff (quart size bag no bigger than their ounce regulation), no knives, firearms, etc. but just other basic things i need to know. Please help