Types of wallets
Custodial wallets, like an exchange account, hold the keys for you. Self custody wallets such as MetaMask, Phantom or a hardware wallet give you the keys. Hot wallets are connected to the internet and convenient; cold wallets keep keys offline and are safer for savings.
Staying safe
Write down your recovery phrase on paper and store it offline. Never type it into a website or share it. Check addresses before sending, and revoke token approvals you no longer need.