I use both online and desktop wallet to store my coin. i store coin that i intend to keep for a long period of time on desktop wallet. i store my bitcoin on electrum wallet. while i store coin i intend to keep for short time on blockchain wallet. i like blockchain because when I am sending bitcoin the fees is low compare to electrum wallet but the desktop feel safer for me and there is privacy.
You should try trezor because it is secure, private keys are generated offline. The attacker cannot access the funds because trezor also generate 24 word seed upon set up and passphrase can be added on it, but if passphrase is forgotten it cannot be recovered. Its good to save big amount of bitcoin.