When the computer is powered down the hard drive's head is immobilized and parked securely, and the platters won't spin unless power is applied to the motor. So I wouldn't worry too much as there is little chance of damage in the "off" state due to shock and vibration. A neoprene sleeve and some clothing around will be plenty enough. Just turn it off, don't put it to sleep and make sure it's sealed so no dust gets in. I put mine in the sleeve then in a Ziplock bag and stash between clothes.

Hard drives are likely to malfunction when they're used and are exposed to shock or vibration, when the parts are moving.

I'd still prefer an SSD though They make computers noticeably faster. Although, they can die too for no apparent reason as well.

If you're worried about losing your pictures due to a hard drive failure then get a large USB Flash Drive and use it for backup.