Where would be the best place to keep my BTC while I'm not trading with it in an exchange?
i guess allmost *any* wallet is more secure than either an online wallet or an exchange wallet. If you don't controll your own private keys, you don't controll your funds...
as mocacinno pointed out, any wallet that lets you control private keys is secure enough
if you use online wallet
(even that gives private keys) you are still essentialy depending on its service, so less secure
desktop/hardware wallet is recommended
I don't feel as if storing it on my own hard drive is very secure as hard drives can fail, and what can you do if that happens..?
with bitcoin core you can backup wallet.dat, but make sure re-backup whenever you change passphrase
for other (HD) wallets you can easily have backup by writing down the mnemonic seed