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Making a Strong (Highly Secure) Password
See the overview of password managers.
Passphrase = a long password of multiple words ideally with mixed case, spaces, punctuation. Passphrase is a preferable term over password because it implies greater length and complexity.
For financial and other sensitive accounts, MPG strongly advises using a complex and reasonably long but memorable passphrase.
Similarly, for a master password for unlocking a password vault with a password manager, you’ll need to imagine up and memorize something, since it must be typed in. But never skimp on a master passphrase, since it unlocks the vault containing all other passwords! See Your Master Password is your defense from Dropbox breaches, real and imagined.
Generating a very strong gibberish password
Being able to memorize and type in a password is ideal, but with a password manager like 1Password, a long gibberish password can be generated and used, since there is no need to type it in.
Use at least 16 characters, but if a site allows it, one might as well use 24 or more characters—it cannot hurt to use more so long as the web site allows it.