I think firstly you should differentiate between exchange and wallet, most of people use exchange for buying and selling and just hold such amount in here through which he can trade, while wallet is mostly for holding coins for long term
Reminder: do not keep your money in online accountsNow there is two type of wallet which are best according to thier security level, like in hardware wallet you should use tezos and ledger while in digital wallet you should use a non-custodial wallet name Electrum..
[LIST] Open Source Hardware WalletsWallets should be open source as if they are close source, you can not verify their codes and they can set back doors in their wallets.
Electrum wallet is free but you have to download it at Electrum official website and it's safer if you verify it before using the wallet software file for installation.
[GUIDE] How to Safely Download and Verify Electrum