I think the safest way to keep them is in a Ledger Nano or a Trezor. Should have max protection.
Yep it's one of the safest way to hold our coins but it has a limited support to the alt coins that we can hold, so sometimes getting a desktop wallet for a specific coin is needed.
MEW for Ethereum and ERC20 tokens, Electrum or Mycelium for Bitcoin and token specific wallets for the ones with their own blockchains. And if you can afford, buy a hardware wallet for extra security!
I'm trusting MEW for Ethereum and my ERC20 coins I'm storing it there and there's no way for someone to hack you unless you will be a victim of phishing links. And be aware about the fake MEW-alike website that has wrong spelling on it's URL.
With bitcoin, I'm good with electrum it's the one that I'm trusting and blockchain.info for smaller amount.