Safest solution would be having a cold storage wallet (offline wallet).
There are a lot of vendors selling such hardware wallets which are considered very safe such as TREZOR or Ledger Nano.
The issue with MEW(MyEtherWallet) is that everything is sent over the internet including your private key. With Hardware Wallets the private keys are generated offline within the device itself. Additionally all transactions are signed with that private key inside the device and what is sent accross the network is the signed transaction.
P.S. Another solution would be to use a Multisig Wallet which has multiple owners and requires multiple signatures to approve transactions. So that if one private key gets compromise you don't loose your funds.