Chainrings and cassette are not worn badly, just rusty. A little TLC and they will look nearly new. Chain is likely toast but that is easy to replace. Good chance that water got into the bottom bracket bearings and they are rusted which is why it feels loose. Either get a BB tool and a new BB, or take it to your shop and have them replace it. Some new cables and housings would make shifting feel much improved. Not going to cost that much to make that bike like new again.