When you say webwallet do you mean an exchange wallet? If so thst is not the best place to store your btc. If they are hacked which has happened btw you can kiss your btc goodbye.
at this point anyone trusting a third party with a decent amount of btc (or other hardware supported coin) is borderline crazy.
now for full disclosure: i still run a hot btc wallet (core wallet) on my 24/7/365 on computer and have for years, since 2011.. this is my original, and still running wallet with a small amount of btc on it for day to day spending. never had it hacked, but im decent with computer security.
as soon as core had passphrases, that went on. ran like that for a couple years. but as soon as i figured out paper wallets and vetted them to my satisfaction, the bulk of my coins went to paper (with passphrases).
now for main storage? trezor one and ledger nano s, with a trezor t on its way. I like the trezor better for various reasons, mainly because i never had a problem accessing coins and never any issues doing firmware updates.
you really need to look into paper and hardware. right now your trust is in a third party. my trust is in myself.
"no private keys? not your coins"