The safest way of keeping bitcoins safe is go for desktop wallet like Electrum, which gives you full rights to use anyway and holding the private keys for bitcoin address is good but in web wallet your wallet is in control of the site owner. So it is not good to keep bitcoin in web wallet and exchange also.
Electrum is a digital wallet since 2011 so it has some reputation on storing btc. But I think if you don't want your coin online and store it like gold and money, cold storage is the best way to do that.
The safest way ever is set up an offline computer with linux, install a wallet downloaded on another pc and make a new address while being offline. Send your coins from all your wallets/addresses to that offline wallet, create a backup copy and store them on a USB drive and boom! You've got yourself a perfectly safe offline storage with a backup in case the computer got damaged or stolen.
Nice advice. I've heard that Linux can be a library that you can arrange what you can do meticulously, but I don't have an experience yet on Linux so I will give this a try.
