If you are currently using a password manager software like 1Password, LastPass, Roboform or iCloud Keychain, you should pick an alternative here.
Bitwarden is a free and open-source password manager. It aims to solve password management problems for individuals, teams, and business organizations. Bitwarden is among the easiest and safest solutions to store all of your logins and passwords while conveniently keeping them synced between all of your devices. If you don't want to use the Bitwarden cloud, you can easily host your own Bitwarden server.
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KeePassXC is a community fork of KeePassX, a native cross-platform port of KeePass Password Safe, with the goal to extend and improve it with new features and bugfixes to provide a feature-rich, fully cross-platform and modern open-source password manager.
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LessPass is a free and open-source password manager that generates unique passwords for websites, email accounts, or anything else based on a master password and information you know. No sync needed. Uses PBKDF2 and SHA-256. It's advised to use the browser addons for more security.
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It is strongly recommended to use a second key besides only a password to log in to all important websites. The first two password managers on this website Bitwarden and KeePassXC already support this feature.
If you store your Time-based One-time Password (TOTP) in the same database as your password, this will alleviate any advantage of two-factor autentication. We believe that storing both together can still be more secure than not using 2FA at all, but to maximize the security gain from using 2FA, you should always store TOTP secrets in a separate database and secure it with a different password.
Under no circumstances should you use an app that does not offer the service to back up your TOTP. Otherwise, if you lose your phone for example, you can also irrevocably lose access to all your Internet accounts.
More information about 2FA can be fount at Two Factor Auth.