Choose a wallet program/app from a reputable list such as https://bitcoin.org/en/choose-your-wallet
Install that wallet program/app on a secure clean PC or phone (as appropriate)
Get the wallet to give you a receive address (nowadays wallets issue a different address each time)
Get your brokerage to transfer money to that address
Get them to tell you the ...
I think many exchanges provide the history and time record of trades, yeah the question is there no completely decentralize exchange exist for now . Lets see can we have any decentralize exchange in future .