Do not know which one is the most secure (there are as many opinions as there are wallets) but you can always choose official selection from
https://bitcoin.org/en/choose-your-wallet Bitcoin core and Armory providing you are willing to download full copy of the blockchain. Electrum or MultiBit where you able to keep your private keys offline and access blockchain on the servers. You can also generate your paper wallet, or use one of the hardware wallets like Trezor.
Each wallet will give you your public key (aka Bitcoin address) where you can send coins to. Technically wallets do not hold coins. Instead, your public / private key hash gets recorded on the blockchain (do not quote me on this) which will keep track of all your transactions, including current balance, so as long as your private keys are kept secure and passwords are difficult to crack any wallet will serve it's intended purpose.
More experienced users can probably be more helpful on the subject as I have only ever used on-line wallet which is a big NO-NO around this forum.