The best way to keep my private keys safe? Best ways means the most reliable and robust, and meanwhile easy to access ways?
The best way currently, that is still easy to access are hardware wallets. The two most famous retailers are:

Trezor:
https://buytrezor.com/

Ledger:
https://www.ledgerwallet.com/

A hardware wallet is dedicated hardware with a defined interface that makes it impossible to extract the private key from the hardware. The interface does however allow signing of transactions. This means that the hardware wallet can safely be plugged into hardware infected with malware.