What hardware wallet would you recommend then? Trezor, Ledger?

How exactly does this work? When you want to sign a transaction you connect this thing to your pc, then press the button on the device and then what happens?

Im quite new to crypto so i wanted to know what exchanges do you use and i'd be grateful for advises on security. I currently keep my crypto on localbitcoins but it recently got hacked to im concerned for my money. I want to move it somewhere safe but still be able to make trades without much fuss. Im still learning to trade but im pretty serious about it. Can you recommend me a good exchange that hasn't been hacked yet?